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MESHING THE MODEL

© 1998–2007 Fluent, Inc. All rights reserved. 3-1

3. MESHING THE MODEL

When you click the Mesh command button on the Operation toolpad, GAM-

BIT opens the Mesh subpad. The Mesh subpad contains command buttons that

allow you to perform mesh operations involving boundary layers, edges,

faces, volumes, and groups.

The symbols associated with each of the Mesh subpad command sets are as

follows.

Symbol Command Set

Boundary Layer

Edge

Face

Volume

Group

The following sections of this chapter describe the commands associated with

each of the command buttons listed above.

Boundary Layers MESHING THE MODEL

3-2 © 1998–2007 Fluent, Inc. All rights reserved.

3.1 Boundary Layers

3.1.1 Overview

Boundary layers define the spacing of mesh node rows in regions immediately

adjacent to edges and/or faces. They are used primarily to control mesh den-

sity and, thereby, to control the amount of information available from the

computational model in specific regions of interest.

As an example of a boundary layer application, consider a computational

model that includes a cylinder representing a pipe through which flows a vis-

cous fluid. Under normal circumstances, it is likely that the velocity gradients

are large in the region immediately adjacent to the pipe wall and small near

the center of the pipe. By attaching a boundary layer to the face that represents

the pipe wall, you can increase the mesh density near the wall and decrease

the density near the center of the cylinder, thereby obtaining sufficient infor-

mation to characterize the gradients in both regions while minimizing the total

number of mesh nodes in the model.

To define a boundary layer, you must specify the following information:

• Boundary-layer algorithm

• Height of the first row of mesh elements

• Growth factor—which specifies the height of each succeeding row of

elements

• Total number of rows—which defines the depth of the boundary layer

• Edge or face to which the boundary layer is attached

• Face or volume that defines the direction of the boundary layer

You can also specify the creation of a transition boundary layer—that is, a

boundary layer for which the mesh node pattern changes with each succeeding

layer. If you specify a transition boundary layer, you must also specify the

transition pattern and number of transition rows.

MESHING THE MODEL Boundary Layers


3.1.2 Boundary Layer Commands

The following commands are available on the Mesh/Boundary Layer subpad.

Symbol Command Description

Create Boundary Layer Creates a boundary layer attached to

an edge or face

Modify Boundary Layer Modifies the definition of an existing

boundary layer

View 3D Boundary Layers Meshes and displays 3-D boundary

layer regions

Modify Label Modifies boundary layer labels

Summarize Boundary Layers Displays existing boundary layers in

the graphics window

Delete Boundary Layers Deletes boundary layers



Create Boundary Layer

The Create Boundary Layer operation (blayer create and blayer

attach commands) defines the spacing of mesh nodes in the vicinity of an

edge or face. The operation requires the following specifications.

• Definition

• Transition pattern

• Attachment

The Definition specifications include the algorithm type and dimension

parameters that determine the shape of the boundary layer, as well as options

that govern the behavior of boundary layers in corner regions. The Transition pattern specifies the arrangement of mesh nodes in the boundary layer region.

The Attachment parameters include the entities to which the boundary layer is

attached and the entities that specify its direction.

Specifying the Definition

To define a boundary layer, you must specify the following parameters:

• Algorithm

• Dimensions

• Internal continuity option

• Corner shape option

The Algorithm specifies the method that GAMBIT uses to determine the gen-

eral shape of the boundary layer. The dimension parameters specify factors

such as the number of boundary layer rows and growth factor. The Internal continuity option specifies the behavior of the boundary layer in regions where it overlaps adjoining boundary layers. The Corner shape option determines the

shape of the mesh in regions surrounding Corner or Reversal vertices that con-nect edges to which boundary layers are attached.



Specifying the Algorithm

The Algorithm specification determines the method that GAMBIT uses to

establish the heights of the elements in the first row of the boundary layer and

compute the heights of all succeeding rows. GAMBIT provides the following

algorithm types.

• Uniform—assigns a uniform height to all first-row elements and uses a

universal growth factor for succeeding rows

• Aspect ratio (first)—computes first-row element heights as a fixed per-

centage of the mesh element widths on the attachment entity and uses

a universal growth factor

• Aspect ratio (last)—assigns a uniform height to all first-row elements

and uses individual growth factors at each attachment-entity mesh

node to determine the size of succeeding rows

Figure 3-1, Figure 3-2, and Figure 3-3 illustrate the differences between the

Uniform, Aspect ratio (first), and Aspect ratio (last) algorithms for a 2-D boundary

layer attached to one edge of a square planar face. In each figure, the attach-

ment edge mesh includes five intervals and a grading ratio of 1.25, and the

boundary layer includes five rows.

Figure 3-1: Uniform boundary layer algorithm (2-D)



Figure 3-2: Aspect ratio (first) boundary layer algorithm (2-D)

Figure 3-3: Aspect ratio (last) boundary layer algorithm (2-D)



For the Uniform boundary layer (Figure 3-1), the first row exhibits a uniform

height across the span of the attachment edge, and the growth factor is

constant; therefore, each succeeding row of elements also exhibits a uniform

height. For the Aspect ratio (first) boundary layer (Figure 3-2), the first-row heights vary in proportion to the edge mesh interval lengths. Consequently,

the first row of the boundary layer grows thicker from left to right across the

edge, because the edge mesh interval lengths increase from left to right. For

the Aspect ratio (last) boundary layer (Figure 3-3), the first row exhibits a uni-form height across the span of the attachment edge, but the growth factor

varies in proportion to the edge mesh interval widths. Consequently, the suc-

ceeding rows grow thicker from left to right across the edge.

� NOTE: If the attachment edge shown in Figure 3-1, Figure 3-2, and Figure

3-3, above, were graded uniformly (Ratio = 1), all three Algorithm options would produce boundary layers of uniform height across the span of the edge.

If you attach a boundary layer to a face (rather than an edge), GAMBIT

applies the definition algorithm along the boundaries of the attachment face.

For example, Figure 3-4 shows an Aspect ratio (first) boundary layer attached to one face of a cube. In this case, the boundary edges of the attachment face

have been premeshed using five intervals and a grading ratio of 1.25.

Figure 3-4: Aspect ratio (first) boundary layer algorithm (3-D)



When attaching a boundary layer to a face, care must be taken to ensure that

the boundary layer is not discontinuous at any vertices on the face boundary.

In Figure 3-4, above, the boundary edges of the attachment face are graded

such that the mesh interval widths on either side of any corner vertex are equal

to each other. As a result, the 3-D boundary layer is continuous at all four cor-

ners of the attachment face. In Figure 3-5, the face boundary edges are graded

such that edge mesh interval lengths differ on either side of three of the four

corner vertices (b, c, and d). Consequently, the boundary layer exhibits dis-

continuities at those vertices.

a

b

c

d

Figure 3-5: Effect of discontinuous grading at face boundary vertices

Specifying the Dimensions

To specify the dimensions of any boundary layer, you must input three

parameters that define its characteristics. The parameters to be specified vary

according to algorithm as follows.

Uniform Algorithm

The Uniform algorithm (see Figure 3-6) definition parameters are as follows.

• First row (a)

• Growth factor (b/a)

• Rows



ba

D

0 1 i–1 i+1 n

~ ~

i

Figure 3-6: Boundary layer dimensions—Uniform algorithm

The First row (a) value specifies the height of the first row (a)—that is, the

absolute distance between the entity to which the boundary layer is attached

and the first row of mesh nodes in the boundary layer. (NOTE: For the Uniform algorithm, the first-row height, a, is uniform across the boundary layer.)

The Growth factor (b/a) value (G) represents the ratio

G b a=

where b is the distance between the first and second rows and a is the height

of the first row. The height of any row in the boundary layer (other than the

first row) is equal to the height of the previous row times the Growth factor (b/a) value.

The Rows value specifies the total number of rows to be included in the

boundary layer.

� NOTE: When you specify the First row (a), Growth factor (b/a), and Rows values, GAMBIT computes the total depth (D) of the boundary layer and dis-

plays the value in the non-editable Depth (D) field on the Create Boundary Layer form.



Aspect ratio (first) Algorithm

The Aspect ratio (first) algorithm (see Figure 3-7) definition parameters are as

follows.

• First percent (a/w)

• Growth factor (b/a)

• Rows

0w 1iw − iw

ia

ic

0 1 i–1 i i+1 n

~ ~

0a

0c

ib

Figure 3-7: Boundary layer dimensions—Aspect ratio (first) algorithm

The First percent (a/w) value specifies the height of any first row boundary

layer node ( ia ) as a percentage of mesh interval width at the associated node

on the attachment entity. For interior nodes on the attachment entity, the gen-

eral specification of first-row height can be expressed as

( )1

100 2

i i

i

w wFa

− + =

where ia is the height of the first row at node i, F is the First percent (a/w)

value, and 1iw − and iw are the widths of the attachment-entity mesh intervals

on either side of node i.



For exterior nodes on the attachment entity (for example, nodes located at

edge endpoints) the first-row heights can be expressed as

0 0100

Fa w

=

and

1100

n n

Fa w −

=

where 0a and na are the heights of the first rows at the exterior nodes.

The Growth factor (b/a) value (G) represents the ratio

i iG b a=

where ib is the distance between the first and second rows at edge mesh node

i and ia is the height of the first row at node i. (NOTE: For the Aspect ratio

(first) algorithm, the Growth factor (b/a) value is constant across the boundary layer.) The height of any boundary layer row at a given edge node is equal to

the height of the preceding row at that node times the growth factor, G.


boundary layer.

� NOTE: When you specify the First percent (a/w), Growth factor (b/a), and Rows values, GAMBIT computes the “last percent” value for the boundary layer

and displays the value in the non-editable Last percent (c/w) field on the Create Boundary Layer form. The Last percent (c/w) value represents the height of the boundary layer top row at any given node relative to the corresponding mesh

interval widths on the attachment entity. The Last percent (c/w) value can be computed from

1RL FG −=

where F and L are the First percent (a/w) and Last percent (c/w) values, respect-ively, G is the Growth factor (b/a) value, and R is the number of Rows.



Aspect ratio (last) Algorithm

The Aspect ratio (last) algorithm (see Figure 3-8) definition parameters are as

follows.

• First row (a)

• Rows

• Last percent (c/w)

0w 1iw − iw0 1 i–1 i i+1 n

~ ~a

ic

0c

ib

Figure 3-8: Boundary layer dimensions—Aspect ratio (last) algorithm

The First row (a) value specifies the height of the first row (a)—that is, the

absolute distance between the entity to which the boundary layer is attached

and the first row of mesh nodes in the boundary layer. (NOTE: For the Aspect ratio (last) algorithm, the first-row height, a, is uniform across the boundary

layer.)


boundary layer.

The Last percent (c/w) value specifies the height of the boundary layer top row at any node relative to the corresponding mesh interval widths on the attach-

ment entity. At any interior mesh node on the attachment entity (for example,

the endpoints of an attachment edge), the relationship between the top row



height ( ic ), the Last percent (c/w) value (L), and the mesh interval widths (w)

can be expressed as

1

100 2

i ii

w wLc − + =

where 1iw − and iw are the widths of the attachment-entity mesh intervals on

either side of node i.

� NOTE: For the Aspect ratio (last) algorithm, the growth factor varies across the

boundary layer and is computed at each mesh node on the attachment entity.

For mesh nodes that are interior to the entity, the growth factor at any node i

can be expressed as

( )1

11

100 2

Ri i

i

w wLG

a

−− + =

where iG is the node-specific growth factor and R is the number of Rows.

Because the growth factor is not constant across the boundary layer, GAMBIT

does not display the Growth factor (b/a) field on the Create Boundary Layer form.

Specifying Internal Continuity

When you attach a boundary layer to a face that constitutes part of a volume,

GAMBIT imprints the boundary layer on all adjoining faces that are also part

of the volume (see Figure 3-9(a)). If you attach boundary layers to two or

more adjoining faces of a volume, the boundary-layer imprints overlap on any

faces that are common neighbors to the adjoining faces (see Figure 3-9(b)).



(a) (b)

Imprints Imprint overlaps

Figure 3-9: Boundary-layer imprints (with shaded attachment faces)

The Internal continuity option on the Create Boundary Layer form determines

the manner in which GAMBIT imprints boundary layers on adjoining faces as

well as the mesh pattern in regions of imprint overlap.

• If you do not select the Internal continuity option, GAMBIT imprints

boundary layers on adjoining faces in the manner described above

(Figure 3-10(a)).

• If you select the Internal continuity option, GAMBIT modifies the

mesh patterns in the overlap regions such that the imprints are dove-

tailed together (see Figure 3-10(b)).



(a) Internal continuity off (b) Internal continuity on

Figure 3-10: Effect of the Internal continuity option

The effect of the Internal continuity option depends, in part, on the values of two GAMBIT default variables:

• MESH.BLAYER.ANGLE_SMOOTH_FACTOR

• MESH.BLAYER.ADJUST_EDGE_BL_HEIGHT

The ANGLE_SMOOTH_FACTOR default variable specifies whether or not the

boundary-layer angling in the corner region is smoothed out across the adja-

cent edges. The ADJUST_EDGE_BL_HEIGHT default variable specifies

whether or not GAMBIT adjusts the boundary layer heights along the adjacent

edges to maintain constant heights with respect to the edges. Each default

variable can take the values 0 (off) and 1 (on).

Figure 3-11 shows the effect of these default variables on the boundary layer

created using the Internal continuity option. In Figure 3-11(a), both variables are set to zero; therefore, the angling of the boundary layer is confined to the

corner region. In Figure 3-11(b), ANGLE_SMOOTH_FACTOR is set to 1; there-

fore, GAMBIT spreads the boundary-layer angling across the entire edge. In

Figure 3-11(c), ADJUST_EDGE_BL_HEIGHT is also set to 1; therefore,

GAMBIT adjusts the boundary-layer heights to maintain constant heights with

respect to the edges adjacent to the corner.



ASF = ANGLE_SMOOTH_FACTOR

AEBH = ADJUST_EDGE_BL_HEIGHT

(a) ASF = 0

AEBH = 0

(b) ASF = 1

AEBH = 0

(c) ASF = 1

AEBH = 1

Figure 3-11: Effect of default variables on Internal continuity option

In addition to affecting the mesh pattern in the imprint-overlap regions, the

Internal continuity option directly affects which types of meshing schemes are

appropriate for volumes to which boundary layers have been applied. For

example, the volume shown in Figure 3-10(b) can be meshed using a Map meshing scheme—resulting in the mesh shown in Figure 3-12(a). By contrast,

the volume shown in Figure 3-10(a) cannot be meshed using a Map scheme,

because the vertex located at the lower right corner of the front face (and

imprint overlap region) is necessarily treated as a Side vertex. To mesh the

volume shown in Figure 3-10(a), it is most reasonable to apply a Pave mesh-

ing scheme to the front face, then apply a Cooper meshing scheme to the

volume, using the front and back faces as source faces (see Figure 3-12(b)).



(a) Map volume mesh

(b) Pave face mesh

Cooper volume mesh

Source faces

Figure 3-12: Effect of Internal continuity option on allowable meshing schemes

Specifying the Wedge Corner Shape

GAMBIT allows you to control the shape of the mesh in the region surround-

ing a Corner or Reversal vertex that connects two edges to which boundary lay-ers are attached. To do so, you must select or unselect (default) the Wedge corner shape option on the Create Boundary Layer form. The Wedge corner shape option produces the following effects (see Figure 3-13):

• If you select the Wedge corner shape option, GAMBIT creates a

wedge-shaped boundary-layer region surrounding the connecting

vertex (Figure 3-13(a)).

• If you unselect the Wedge corner shape option, GAMBIT creates a

block-shaped boundary-layer region surrounding the connecting vertex

(Figure 3-13(b)).

If two edges meet at a Corner or Reversal vertex, and each edge possesses a separate boundary layer, then to create a wedge-shaped boundary layer at the

corner, you must select the Wedge corner shape option when creating each separate boundary layer.



(a) Wedge corner shape on (b) Wedge corner shape off

Figure 3-13: Effect of Wedge corner shape option

Specifying the Transition Characteristics

The boundary-layer transition characteristics consist of two components:

• Transition pattern

• Number of transition rows

Specifying the Transition Pattern

The transition pattern determines the arrangement of mesh nodes in the

region near the outermost row of the boundary layer. Boundary layer transi-

tion patterns are defined by the ratio

A:B

where B is the number of mesh intervals in a given row and A is the number of

mesh intervals in the immediately preceding full row. GAMBIT allows you to

specify any of four transition patterns—1:1, 4:2, 3:1, or 5:1.

Figure 3-14 shows four different two-row boundary layers representing each

of the four transition patterns listed above.



(a) 1:1 (b) 4:2

(c) 3:1 (d) 5:1

Figure 3-14: Boundary layer transition patterns

� NOTE: Edges can host any of the four transition patterns, but faces can host

only the 1:1 transition pattern.

Specifying the Number of Transition Rows

When you specify any transition pattern other than 1:1, you must also specify

the number of transition rows—that is, the number of outermost rows to

which the transition pattern is applied. GAMBIT applies the 1:1 pattern to all rows other than the transition rows. Figure 3-15 shows the effect of the num-

ber of transition rows on a boundary layer consisting of three rows with the

transition pattern 4:2.



(a) One transition row (b) Two transition rows

Figure 3-15: Effect of number of transition rows

Specifying the Attachment Entity

To define the location of a boundary layer, you must specify the edge or face

to which the boundary layer is attached. If the edge or face is shared by two or

more faces or volumes, respectively, you must also specify the face or volume

that defines the direction of the boundary layer. For example, each edge of a

rectangular brick volume is shared by two rectangular faces. If you attach a

boundary layer to one of the edges of the volume, you must specify which of

the corresponding faces defines the direction of the boundary layer.

Specifying the Boundary Layer Direction

When you specify an edge or face to which to attach a boundary layer,

GAMBIT highlights the edge or face in the graphics window and displays the

following items:

• The boundary layer as currently specified

• An arrow that indicates the direction of the boundary layer

You can change the direction of the boundary layer either by means of the

Attachment (Edge or Face) list box on the Create Boundary Layer form or by

means of the mouse.



� NOTE: If the boundary-layer attachment entity serves as an attachment entity

for a size function or is part of a higher-topology entity to which a size func-

tion is attached, GAMBIT might or might not reflect the size-function defini-

tion in the temporary display of the boundary layer. Specifically, the

boundary-layer display reflects the definition of the size function only if the

background grid for the size function has already been generated—for

example, by meshing an edge that is also part of the size-function attachment

entity.

Changing Direction by Means of the List Box

When you specify an edge or face in the Attachment list box on the Create Boundary Layer form, the list box displays both the specified entity itself and

the face or volume that defines the direction of the boundary layer. To change

the direction of the boundary layer by means of the list box, you can perform

either of the following operations.

1. Specify the edge or face again in the Attachment list box

2. Use the Edge List or Face List paired pick-list form to specify the entity

and direction of the boundary layer (see “Using the Edge List or Face

List Form,” below).

Changing Direction by Means of the Mouse

To change the direction of the boundary layer by means of the mouse, Shift-

middle-click the entity to which the boundary layer is attached.

Specifying Multiple Boundary Layers

GAMBIT allows you to apply a given boundary layer definition to more than

one edge or face at a time. To do so, you must include in the Attachment entity pick list all of the entities to which the currently defined boundary layer is to

be attached.

You can add an edge or face to the Attachment entity pick list on one of the following ways:

• Input the entity name directly in the Attachment list box or select the entity from the entity pick-list form

• Pick the entity in the graphics window



Smoothing the Mesh at Boundary Layer Transition Points

If you attach 2-D boundary layers to adjacent edges that share a common face

or attach 3-D boundary layers to adjacent faces that share a common volume,

GAMBIT automatically smoothes the resulting mesh at the transition points

between the boundary layers. You can control the range of elements over

which the boundary layers are smoothed by means of the HEIGHT_TRANSIT_

RATIO default variable.

As an example of mesh smoothing at boundary layer transition points, con-

sider the 2-D boundary layers shown in Figure 3-16. In this case, the boundary

layers are attached to adjacent edges that constitute one side of a square face.

They differ from each other only with respect to their growth factors.

Figure 3-16: Example 2-D boundary layers on adjacent edges

If you retain the default value for the HEIGHT_TRANSIT_RATIO default

variable and mesh the face shown in Figure 3-16, GAMBIT creates the mesh

shown in Figure 3-17. In this case, the discontinuity between the boundary

layers is smoothed over three intervals on either side of the transition point.



Transition region (3 intervals/side)

Figure 3-17: Mesh with boundary layer smoothing at transition point

As noted above, you can use the HEIGHT_TRANSIT_RATIO default variable

to control the number of intervals over which the mesh is smoothed. The

effect of the default variable depends on whether its value is greater or less

than one (1) and can be summarized as follows:

• HEIGHT_TRANSIT_RATIO ≤ 1—Fraction of total intervals on either

side of the transition point

• HEIGHT_TRANSIT_RATIO > 1—Number of transition intervals on

either side of the transition point

By default, the HEIGHT_TRANSIT_RATIO value is equal to 0.5; therefore, the

boundary layer is smoothed over half of the intervals on each side of the

transition point (see Figure 3-17, above). If you specify a HEIGHT_TRANSIT_

RATIO value greater than one (1), GAMBIT rounds the value up or down to

the closest integer and uses the rounded value as the number of intervals on

either side of the transition point over which the mesh is smoothed. For

example, if you specify a value of 2 for the default variable, GAMBIT

smoothes the mesh as shown in Figure 3-18.



Transition region (2 intervals/side)

Figure 3-18: Boundary layer smoothing—HEIGHT_TRANSIT_RATIO = 2

In this case, the mesh is smoothed over a distance of two intervals on either

side of the transition point.



Using the Create Boundary Layer Form

To open the Create Boundary Layer form (see below), click the Create Boundary Layer command button on the Mesh/Boundary Layer subpad.

The Create Boundary Layer form contains the following specifications.

�� Show displays the boundary layer(s) in the graphics window as they

are created and defined.



Definition Specifications

Definition: —————————————————————————

Algorithm: contains radio buttons that specify the boundary layer

definition algorithm. GAMBIT provides the following

algorithm options.

• Uniform

• Aspect ratio (first)

• Aspect ratio (last)

For a description of the algorithm options, see “Specifying

the Algorithm,” above.

The definition specifications differ according to Algorithm option as follows.

Uniform Algorithm Specifications

When you specify the Algorithm:Uniform option, GAMBIT displays the

Definition fields as shown on the Create Boundary Layer form, above.

First row (a) specifies the height of the boundary layer first row.

Growth factor (b/a)

–��–

specifies the growth factor—that is, the ratio of the

height of each row relative to that of the preceding row.

Rows –��– specifies the total number of rows in the boundary layer.

Depth (D) displays (non-editable field) the total depth of the

boundary layer.



Aspect ratio (first) Algorithm Specifications

When you specify the Algorithm:Aspect ratio (first) option, GAMBIT displays

the following Definition fields on the Create Boundary Layer form.

First percent (a/w) specifies the height of the boundary layer first row as a

percentage of the edge element width on the attachment

entity.

Growth factor (b/a)

–��–

specifies the growth factor—that is, the ratio of the

height of each row relative to that of the preceding row.


Last percent (c/w) displays (non-editable field) the height of the top row as

a percentage of the average interval width.



Aspect ratio (last) Algorithm Specifications

When you specify the Algorithm:Aspect ratio (last) option, GAMBIT displays

the following Definition fields on the Create Boundary Layer form.

First row (a) specifies the height of the boundary layer first row.


Last percent (c/w) specifies the height of the top row as a percentage of the

average interval width.

General Specifications

The following Definition specifications are common to all of the Algorithm options.

�� Internal continuity

specifies that boundary-layer imprints are dovetailed in

overlapping regions (see “Specifying Internal Continuity,”

above).

�� Wedge corner shape

specifies that the boundary-layer forms a wedge shape in

the region surrounding a Corner or Reversal vertex (see “Specifying the Wedge Corner Shape,” above).



Transition Pattern Specifications

Transition Pattern:

contains four radio buttons that specify the transition pattern.

The pattern options are 1:1, 4:2, 3:1, and 5:1. (See “Specifying the Transition ,” above.)

Transition –��–

Rows

specifies the number of transition rows for transition pat-

terns 4:2, 3:1, and 5:1. (NOTE: You must use the slide bar,

rather than the associated text box, to set the number of

transition rows.)

Attachment Specifications

Attachment: —————————————————————————

Edges � Faces

specifies whether the boundary layer is attached to an edge

or a face.

Edges �

Faces

specifies the edge or face to which the boundary layer is

attached. (NOTE: When you click the pick list button

on the Attachment entity list box, GAMBIT opens a

paired pick list form titled Edge List or Face List. For instructions in using the paired pick list form, see

“Using the Edge List or Face List Form,” below.)

Label specifies a label for the boundary layer.



Using the Edge List or Face List Form

When you specify an edge or face to which a boundary layer is attached,

GAMBIT adds the edge or face to a paired pick list. The paired pick list

includes both the attachment entity itself (edge or face) and the entity that

defines the direction of the boundary layer (face or volume). You can modify

the edge or face paired pick list by means of either the Edge List or Face List pick-list form, respectively. Both forms operate according to the following

general principles described for the Edge List form.

To open the Edge List form (see below), select Edge in the Attachment field on the Create Boundary Layer form and click the associated pick list button.

The Edge List paired pick-list form operates in a manner similar to that of con-

ventional pick-list forms (see GAMBIT User’s Guide, Chapter 3). It differs

from the conventional forms only in that the Picked scroll list includes two columns.

• The left column lists the edge to which the boundary layer is attached.

• The right column lists the face that defines the direction of the bound-

ary layer.



When you add an edge to the Picked scroll list by means of the right-arrow

command button, GAMBIT adds the edge to the Edge column and automati-

cally includes one of its associated faces in the Face column. (The face defines

the direction of the boundary layer.) If you add the same edge again to the

Picked scroll list, GAMBIT creates a second entry for the edge in the Edge column and includes another of its associated faces in the Face column. When

the Face column includes all faces associated with a given edge, GAMBIT

removes that edge from the Available column.



Modify Boundary Layer

The Modify Boundary Layer operation (blayer modify and blayer

attach commands) modifies the specifications for any existing boundary

layer.

Using the Modify Boundary Layer Form

To open the Modify Boundary Layer form (see below), click the Modify Bound-ary Layer command button on the Mesh/Boundary Layer subpad.

(For a description of the options and specifications available on the Modify Boundary Layer form, see “Create Boundary Layer,” above.)



View 3D Boundary Layers

The View 3D Boundary Layers operation (blayer mesh command) allows

you to examine volume meshes in regions affected by 3-D boundary layers.

When you execute the View 3D Boundary Layers command for any 3-D

boundary layer, GAMBIT meshes the volume associated with the boundary

layer, renders the mesh invisible outside the boundary layer region, and auto-

matically opens the Examine Mesh form.

Figure 3-19 illustrates the effect of the View 3D Boundary Layers operation for a cube with a uniform boundary layer attached to two adjoining faces. In this

case, the boundary layer was created using the Internal continuity option; therefore, the boundary layer dovetails in its overlapping regions.

(a) Cube with boundary layer (b) Boundary layer view

Figure 3-19: View 3D Boundary Layers operation

If you execute the View 3D Boundary Layers operation for the boundary layer shown in Figure 3-19(a), GAMBIT meshes the cube, renders the mesh invisi-

ble outside the boundary layer region, and automatically opens the Examine Mesh form to display the mesh (Figure 3-19(b)). By default, GAMBIT selects

the Range option on the Examine Mesh form and displays all volume elements

in the boundary layer region; however, you can use any of the Examine Mesh options (for example, Plane or Sphere) to customize the mesh display.



� NOTE: It is advisable to close the Examine Mesh form before executing subse-

quent GAMBIT operations. When you close the Examine Mesh form,

GAMBIT automatically executes an undo command to undo the blayer

mesh command that generated the boundary layer mesh(es).

Using the View 3D Boundary Layers Form

To open the View 3D Boundary Layers form (see below), click the View com-

mand button on the Mesh/Boundary Layer subpad.

The View 3D Boundary Layers form includes the following specification.

B.L.s � specifies the boundary layer region(s) to be displayed.



Modify Boundary Layer Label

The Modify Boundary Layer Label operation (blayer modify command)

changes the label associated with any boundary layer.

Using the Modify Boundary Layer Label Form

To open the Modify Boundary Layer Label form (see below), click the Modify Label command button on the Mesh/Boundary Layer subpad.

The Modify Boundary Layer Label form includes the following specifications.

B.L. � specifies the boundary layer to be modified.

Label specifies a new label for the boundary layer.



Summarize Boundary Layers

The Summarize Boundary Layers operation (blayer summarize command)

displays one or more existing boundary layers in the graphics window.

Using the Summarize Boundary Layers Form

To open the Summarize Boundary Layers form (see below), click the Summa-rize command button on the Mesh/Boundary Layer subpad.

The Summarize Boundary Layers form contains the following specification.

B.L.s � specifies the boundary layer(s) for which summary information

is to be displayed.



Delete Boundary Layers

The Delete Boundary Layers operation (blayer delete command) deletes

one or more existing boundary layers.

Using the Delete Boundary Layers Form

To open the Delete Boundary Layers form (see below), click the Delete com-

mand button on the Mesh/Boundary Layers subpad.

The Delete Boundary Layers form includes the following specification.

B.L.s � specifies the boundary layer(s) to be deleted.

Edge Meshing Commands MESHING THE MODEL


3.2 Edge Meshing Commands

The following commands are available on the Mesh/Edge subpad.


Mesh Edges Creates mesh nodes along edges

Set Edge Element Type Specifies edge element types used

throughout the model

Link Edge Meshes Unlink Edge Meshes

Creates and deletes mesh hard links

between edges

Split Meshed Edge Splits an edge at a mesh node

Summarize Edge Mesh Displays mesh grading information

Delete Edge Meshes Deletes existing mesh nodes from

edges

The following sections describe the purpose and operation of each of the

commands listed above.

MESHING THE MODEL Edge Meshing Commands


3.2.1 Mesh Edges

The Mesh Edges operation (edge mesh, edge modify, edge picklink,

and edge pickunlink commands) grades or meshes any or all edges in the

model. When you grade an edge, GAMBIT applies the mesh node spacing

specifications but does not create mesh nodes on the edge. When you mesh an

edge, GAMBIT creates mesh nodes according to the specifications.

To perform a grading or meshing operation, you must specify the following

parameters:

• Edge(s) to which the grading specifications apply

• Grading scheme

• Mesh node spacing (number of intervals)

• Edge meshing options

Specifying Edges

When you specify one or more edges for a grading or meshing operation, you

must specify the following options:

• Soft-link

• Reverse

When you soft-link two or more edges, GAMBIT links the edges for meshing

purposes so that any grading or meshing specifications applied to one edge

can be simultaneously applied to the other edges as well. When you reverse an

edge, GAMBIT reverses the sense of the edge; therefore, any directional

grading scheme associated with the edge is also reversed.

In addition to the soft-link and reverse options described above, GAMBIT

allows you to specify whether or not to impose the grading parameters of the

first edge specified in the Edges list on all other parameters in the list (see

“Imposing First-Edge Grading and Spacing Parameters,” below).

Soft-linking Edges

When you specify more than one edge for a grading or meshing operation,

GAMBIT allows you to create soft links between the specified edges. When

you grade or mesh an edge that is soft-linked to other edges, you can simulta-

neously apply the grading or meshing specifications to all of the edges that are

soft-linked to the specified edge.



Forming, Maintaining, and Breaking Soft Links

When you specify two or more edges for a grading or meshing operation, you

must specify the status of any soft links that involve the edges. The three soft-

link status options are as follows:

• Form—forms soft links between the edges

• Maintain—maintains all existing soft links that involve the edges

• Break—breaks any existing soft links that involve the edges

When you Form soft links between two or more edges, GAMBIT creates a

“chain” of links between the specified edges. If you form a soft link involving

an edge that is part of an existing soft-link chain, GAMBIT breaks the existing

soft link associated with the edge. That is, no single edge is allowed to consti-

tute part of more than one soft-link chain.

When you Maintain soft links, GAMBIT does not form or break any existing

soft links associated with the specified edge(s).

When you Break a soft link associated with an edge, GAMBIT removes the

edge from the soft-link chain but does not break any other soft links in the

chain. That is, any other edges that are part of the soft-link chain remain soft-

linked to each other.

Grading or Meshing Soft-link Chains

When you grade or mesh an edge that constitutes part of an existing soft-link

chain, GAMBIT allows you to specify whether the grading or meshing speci-

fications apply to all edges that belong to the chain (the Pick with links option). The general rules pertaining to the Pick with links option are as follows.

• To grade or mesh all edges that belong to an existing chain, select the

Pick with links option on the Mesh Edges form and specify one of the

edges that belongs to the chain.

• To grade or mesh an edge that constitutes part of a soft-link chain

without grading or meshing the other edges in the chain, unselect the

Pick with links option before specifying the edge. To maintain all links

between the specified edge and all edges to which it is soft-linked,

select the Soft links:Maintain option before specifying the edge.



Reversing Edges

When you mesh an edge using a non-uniform grading scheme, GAMBIT

grades or meshes the edge relative to its sense. For example, if you mesh an

edge using a First Length scheme (see below) and specify a first interval length

of 2, GAMBIT locates the first mesh node at a distance of 2 units from the

edge start vertex.

When you specify edges for a grading or meshing operation, GAMBIT allows

you to change their respective senses by means of the Reverse command

button on the Mesh Edges form. If you reverse the sense of an edge the grad-

ing of which is non-uniform, the grading or meshing scheme is also reversed.

For example, if you mesh an edge using a First Length grading scheme and

specify a first interval length of 2, then click Reverse to reverse the sense of the edge, GAMBIT meshes the edge such that the last mesh node is located at

a distance of 2 from the edge end vertex.

If you apply the Reverse option to an edge that is part of a soft-link chain and select the Pick with links option, GAMBIT reverses the sense and, therefore,

the grading of all edges in the chain.

Imposing First-Edge Grading and Spacing Parameters

When you specify a set of edges for grading and/or meshing, you can also

determine whether or not to impose the grading parameters of the first edge

specified in the Edges list on all other edges in the list. To impose the first-

edge grading and/or spacing parameters on the other specified edges, you

must select the Use first edge settings option on the Mesh Edges form. By

default, the Use first edge settings option is selected.

Grading Parameters

If you specify a set of edges at least one of which differs from the others with

respect to its Grading parameters, the Use first edge settings option produces the following effects on the Grading section of the Mesh Edges form.

• If you select the Use first edge settings option, the Grading settings remain active and display the settings of the first edge specified in the

Edges list.

• If you unselect the Use first edge settings option and select an edge the grading parameters of which differ from the currently displayed para-

meters, the Grading settings become inactive and the displayed settings

are those of the most recently selected edge.



Spacing Parameters

The behavior of the Spacing section of the Mesh Edges form is identical to

that of the Grading section (see above) with respect to the Use first edge settings option.

� NOTE: The Grading and Spacing sections of the Mesh Edges form behave

independently of each other with respect to the Use first edge settings option.

Specifying the Grading Scheme

GAMBIT provides the following types of edge mesh grading schemes.

• Successive Ratio

• First Length

• Last Length

• First Last Ratio

• Last First Ratio

• Exponent

• Bi-exponent

• Bell Shaped

The first six schemes listed above are non-symmetric schemes—that is, they

can produce grading patterns that are not necessarily symmetric about the

center of the edge. The last two schemes are symmetric schemes—that is, they

are constrained to produce grading patterns that are symmetric about the

center of the edge.



� NOTE: When you grade or mesh an edge that is connected to one or more

edges that are already graded or meshed, GAMBIT provides the means to

ensure that the new grading is similar to the existing grading(s) in the

region(s) surrounding the connecting vertex (or vertices). This specification is

accomplished by means of the MESH.EDGE.FLEXIBLE_GRADING default

variable.

• If you set the variable to 0 (default), GAMBIT applies the settings speci-

fied on the Mesh Edges form without regard to the existing grad-

ing/meshing parameters(s) on the already graded or meshed edges.

• If you set the variable to 1, GAMBIT ignores the settings specified on

the Mesh Edges form and grades the edge such that its first interval

length in the region adjacent to the connecting vertex is similar to that on

the already meshed or graded edge(s) to which it is connected. If the

edge is connected to graded/meshed edges at both endpoint vertices,

GAMBIT uses a single-sided grading scheme the first and last interval

lengths of which are similar to the lengths of the intervals on the edges

to which it is connected (on each end). If the edge is connected to multi-

ple graded or meshed edges at a single vertex, GAMBIT averages the

lengths on the graded/meshed edges in the region surrounding the con-

necting vertex to determine the appropriate first interval length on the

ungraded edge.

Non-Symmetric Grading Schemes

For each of the non-symmetric grading schemes, GAMBIT positions mesh

nodes along the edge such that the ratio of any two succeeding interval lengths

is constant. That is,

Rl

l

i

i =+1

where il and 1+il are the lengths of intervals i and i+1, respectively, and R is a

fixed value (see Figure 3-20). For any given number of intervals (n), the grad-

ing schemes differ from each other only with respect to the manner in which

GAMBIT determines the value of the interval length ratio, R.



. . .

Start End

Interval lengths

Mesh node location

Constant1 ==+ Rl

l

i

i

1l 2l 3l 1−nl nl

Figure 3-20: Edge mesh grading parameters

� NOTE: When you mesh an edge, GAMBIT positions the mesh nodes based,

in part, on the edge element type as currently specified on the Set Edge Element Type form (see “Set Edge Element Type,” below).

• If you specify 2-node edge elements, GAMBIT creates mesh nodes

only at the endpoints of the edge mesh intervals.

• If you specify 3-node edge elements, GAMBIT creates an additional

mesh node at the center of each mesh interval.

For example, if you specify the 3-node edge element type and grade an edge

such that it includes five mesh intervals, GAMBIT creates 11 mesh nodes on

the edge. Six of the mesh nodes define the endpoints of the mesh intervals; the

other five are located at the centers of the intervals.

The mesh node locations presented throughout this section are based on the

2-node edge element type.



Grading Scheme Input Parameters

For all non-symmetric grading schemes other than the Exponent scheme, the

interval length ratio, R, is a function of the following parameters:

• Total edge length, L

• Number of intervals, n

• Length of the first interval ( 1l ) or last interval ( nl ) on the edge

For the Exponent scheme, R is a function of L, n, and a user-specified input

parameter, x.

The following table lists the formulas that GAMBIT uses to determine the

interval length ratios (R) for each of the non-symmetric grading schemes. The

table also lists the pertinent input parameters and the corresponding titles of

the input fields on the Mesh Edges form.

Scheme Formula Parameter Field Title

Successive Ratio None R Ratio

First Length

11

1

l

LR

n

i

i =∑−

− 1l Length

Last Length

n

n

i

ni

l

LR =∑

−

−

1

nl Length

First Last Ratio ( )1/1

1

−−

=

n

nl

lR

nl

l1 Ratio

Last First Ratio ( )1/1

1

−

=

n

n

l

lR

1l

ln Ratio

Exponent ( )( )2

1−=

xn

L

eR x Ratio



As an example of the differences between input parameters for the non-sym-

metric grading schemes, consider the straight, graded edge shown in Figure

3-21. The edge possesses a length of 15 units (L = 15) and is to be graded

such that it contains four intervals (n = 4), each of which is twice as long as

the previous interval (R = 2).

Edge length: L = 15

Number of intervals: n = 4

Ratio: R = 2

Start End

11 =l 22 =l 84 =l43 =l

Figure 3-21: Edge grading example

The grading parameters required by each of the non-symmetric schemes to

create the grading shown in Figure 3-21 are as follows.

Scheme Ratio Length

Successive Ratio 2

First Length 1

Last Length 8

First Last Ratio 0.125

Last First Ratio 8

Exponent 0.6848



Double-Sided Grading

When you grade or mesh an edge using any non-symmetric scheme other than

the Last Length or Exponent schemes, GAMBIT allows you to specify whether

the grading scheme is single-sided or double-sided. (NOTE: To apply an Expo-nent scheme to two segments of a single edge, use the Bi-exponent symmetric

grading scheme (see below).) Double-sided grading differs from single-sided

grading in that the edge is divided into two separate segments for grading

purposes, and each segment is graded according to its own grading parameter.

(NOTE: GAMBIT does not allow you to specify different grading schemes

for each segment.)

Center of Grading

When you specify double-sided grading, GAMBIT positions either a node or

an interval at the center of grading for the edge. The form of the grading

center (node or interval) depends on the total number of edge intervals (n) as

follows (see Figure 3-22).

• If n is even, GAMBIT locates a mesh node at the center of grading.

• If n is odd, GAMBIT locates a mesh interval at the center of grading.

Start End

Center node (n even)

. . . . . .

Segment 1 Segment 2

Start End

Center interval (n odd)

. . . . . .

Segment 1Segment 2

1,

1,1

1

i

i

l

lR

+=2,

2,1

2

i

i

l

lR

+=

1,1l 1,2l 1,nl ′ 2,nl ′ 2,2l 2,1l

1,1l 1,2l 2,2l 2,1l2,1, , nn ll ′′

Figure 3-22: Double-sided grading—location of grading center



The location of the center node (n even) or the location and size of the center

interval (n odd) is determined according to the following rules.

• If n is even, GAMBIT grades the edge such that the lengths of the

intervals on either side of the center node are equal.

• If n is odd, GAMBIT grades the edge such that the length of the center

interval conforms to the meshing parameters specified for both seg-

ments of the edge.

As an example of the effect of interval number on double-sided grading, con-

sider the edge shown in Figure 3-23. The edge possesses a length of 8 units

and is to be graded such that 1R = 1.5 and 2R = 1.0.

Start End

511,

1,1

1 .l

lR

i

i == +01

2

21

2 .l

lR

i,

,i == +

8=L

Figure 3-23: Double-sided grading scheme—example

Figure 3-24 and Figure 3-25 show the effect of specifying 7 and 8 intervals,

respectively, on the grading of the edge shown in Figure 3-23.



Start End

Center interval

n = 7

511 .R =

011 .R =

1,1l 1,2l 1,3l 2,41,4 ll = 2,3l 2,2l 2,1l

Figure 3-24: Double-sided grading scheme, n = 7

Start End

Center node

n = 8

511 .R =

011 .R =

1,1l 1,2l 1,3l 2,3l 2,2l 2,1l1,4l 2,4l

Figure 3-25: Double-sided grading scheme, n = 8



The following table lists the interval lengths for the double-sided grading

schemes shown in Figure 3-24 and Figure 3-25.

Interval Figure 3-24 (n = 7) Figure 3-25 (n = 8)

1 0.44 0.37

2 0.66 0.56

3 0.99 0.83

4 1.48 1.25

5 1.48 1.25

6 1.48 1.25

7 1.48 1.25

8 1.25

Note that, if you specify seven intervals for the edge (n = 7), GAMBIT grades

the edge such that the length of the center interval satisfies the grading ratios

for both edge segments (see Figure 3-24). That is,

48.12,41,4 == ll

5.199.0

48.1

1,3

1,4 ==l

l

and 0.148.1

48.1

2,3

2,4 ==l

l .

If you specify eight intervals for the edge (n = 8), GAMBIT grades the edge

such that the lengths of the intervals on either side of the center node are equal

(see Figure 3-25). That is,

25.12,41,4 == ll

5.183.0

25.1

1,3

1,4 ==l

l

and 0.125.1

25.1

2,3

2,4 ==l

l .



Double-Sided Grading Input Parameters

When you grade or mesh an edge by means of a double-sided grading scheme,

you must specify grading parameters for both segments of the edge. The fol-

lowing table lists double-sided grading input parameters as they appear on the

Mesh Edges form for each of the available grading schemes. (For descriptions

of the parameters, see Figure 3-22.)

Scheme Parameter Field Title

Successive Ratio 1R

2R

Ratio 1

Ratio 2

First Length 1,1l

2,1l

Length 1

Length 2

First Last Ratio

1,

1,1

nl

l

′

2,

2,1

nl

l

′

Ratio 1

Ratio 2

Last First Ratio

1,1

1,

l

ln′

2,1

2,

l

ln′

Ratio 1

Ratio 2

As an example of the specification of double-sided grading input parameters,

consider the examples shown in Figure 3-24 and Figure 3-25, above. The fol-

lowing tables list the parameters that are required to create the grading

schemes shown in the figures.



Double-sided grading input parameters, Figure 3-24 (n = 7):

Scheme Ratio 1 Ratio 2 Length 1 Length 2

Successive Ratio 1.5 1

First Length 0.44 1.48

First Last Ratio 0.297 1

Last First Ratio 3.36 1

Double-sided grading input parameters, Figure 3-25 (n = 8)

Scheme Ratio 1 Ratio 2 Length 1 Length 2

Successive Ratio 1.5 1

First Length 0.37 1.25

First Last Ratio 0.297 1

Last First Ratio 3.36 1

Symmetric Grading Schemes

GAMBIT provides two symmetric grading schemes for edge meshing:

• Bi-exponent

• Bell Shaped

Both schemes grade a given edge such that mesh node placement is symmetric

about the center of the edge. The schemes differ from each other in the man-

ner in which GAMBIT determines the mesh node spacing along the edge.

Bi-Exponent Scheme

The Bi-exponent scheme divides the edge into two segments of equal length

and applies the Exponent grading scheme separately to each segment. The

Exponent input parameter, x—specified by means of the Ratio field on the Mesh Edges form—produces the following grading characteristics for the Bi-exponent scheme.



x Grading Characteristic

< 0.5 Mesh nodes are densest near the center of grading and least

dense near the endpoints of the edge.

= 0.5 Mesh nodes are evenly spaced along the entire edge.

> 0.5 Mesh nodes are densest near the endpoints of the edge and

least dense near the center of grading.

Bell Shaped Scheme

The Bell Shaped scheme grades the edge such that the mesh node density

obeys a normal distribution centered at the geometric center of the edge. The

user-specified input parameter for the Bell Shaped scheme—specified by

means of the Ratio field on the Mesh Edges form—produces grading charac-

teristics identical to those shown above for the Bi-exponent scheme.

Specifying Node Spacing

The interval length ratio, R, is a function of both the edge length, L, and the

number of intervals, n (see above). GAMBIT provides three different ways to

specify the number of intervals on an edge.

• Interval count

• Interval size

• Shortest edge (%)

Interval Count

When you select the Interval count option, you must input the actual number of

mesh intervals to be placed on the edge. GAMBIT grades or meshes the edge

with enough nodes to result in the specified number of intervals. That is,

1+= nm

where m is the total number of mesh nodes on the edge, including the end-

points. For example, if you specify an interval count of 6 (n = 6), GAMBIT

grades or meshes the edge with 7 nodes (m = 7), thereby creating 6 intervals

on the edge.



Interval Size

When you select the Interval size option, you must input an interval length.

GAMBIT uses the interval length to determine the total number of intervals

on the edge according to the following equation:

d

Ln =

where n is the number of intervals on the edge, L is the edge length, and d is

the interval size (user input). If n is a non-integer, GAMBIT rounds to the

nearest whole number to determine the number of intervals on the edge.

Shortest Edge (%)

When you select the Shortest edge (%) option, you must input an interval size

value expressed as a percentage of edge length. GAMBIT calculates the

global interval size (d) for the current edge-meshing operation as follows:

min100

Lx

d

=

where x is the Shortest edge (%) input value, and minL is the length of the short-

est edge currently existing in the entire model. (NOTE: When you select the

Shortest edge (%) option, GAMBIT highlights the graphics window display of

the shortest edge.)

GAMBIT uses the resulting value of d to calculate the total numbers of inter-

vals for all edges specified for the current edge-meshing operation. For exam-

ple, if the shortest edge in the model is 10 units in length, and you mesh an

edge that is 30 units long and specify the Shortest edge (%) option with x = 20 (%), GAMBIT calculates the number of intervals, n, on the meshed edge as

follows:

( )15

10100

20

3030=

=

=d

n .

Therefore, GAMBIT creates 15 intervals on the meshed edge.



Specifying Edge Meshing Options

GAMBIT provides the following edge meshing options:

• Mesh

• Remove old mesh

• Ignore size functions

If you select the Mesh option, GAMBIT creates mesh nodes when it applies

the grading specifications listed on the Mesh Edges form. If you Apply the cur-rently specified parameters without selecting the Mesh option, GAMBIT

applies the node distribution parameters to the edge(s) but does not create

mesh nodes.

If you select the Remove old mesh option, GAMBIT deletes any currently

existing mesh and/or grading information from the specified edge(s).

If you select the Ignore size functions option, GAMBIT ignores any existing

size-function specifications that would otherwise affect the edge mesh.

� NOTE: If you attempt to grade or mesh an edge that serves directly as an

attachment entity for an existing size function or is part of a higher-topology

entity that serves as an attachment entity for a size function, GAMBIT sus-

pends the temporary display of edge mesh nodes until the background grid is

generated. For example, if you attach a size function to a brick-shaped volume

and attempt to grade or mesh one of the volume edges before meshing the

volume, GAMBIT suspends the temporary display of mesh nodes for the

edge. However, if you mesh one of the other edges before attempting to grade

or mesh the edge (thereby generating the background grid for the size func-

tion), GAMBIT enables the temporary display of mesh nodes for the edge.

To enable the temporary display of the mesh nodes and assign the specified

grading parameters to an edge such as that described above, you must select

the Ignore size functions option on the Mesh Edges form.



Using the Mesh Edges Form

To open the Mesh Edges form (see below), click the Create Mesh command

button on the Mesh/Edge subpad.

The Mesh Edges form contains the following options and specifications.

Edge and Soft-link Specifications

Edges � specifies one or more edges to which the currently specified

grading and/or meshing operations apply.

�� Pick with links

specifies that all edges hard-linked or soft-linked to the picked

edge(s) are graded and/or meshed according to the currently

specified grading scheme.



Reverse reverses the sense and grading of all specified edges.

NOTE: If the Pick with links option is selected (see above), the Reverse command button reverses the sense of all edges

selected by means of the Edges list box as well as all edges linked to those edges.

Soft link —————————————————————————

Form � Break Maintain

specifies whether soft links are formed, broken, or main-

tained during the edge meshing process.

• Form—forms soft links between all specified edges

• Break—breaks existing soft links associated with

the specified edges

• Maintain—maintains all current soft links

�� Use first edge settings

imposes the grading and spacing parameters of the first edge

specified in the Edges list on all other edges in the list.

Grading —————————————————————————

�� Apply specifies that the currently displayed grading specifications

are applied to all picked edges.

Default resets grading specifications to their default values.

Type ————————————————————————

Successive Ratio � First Length Last Length First Last Ratio Last First Ratio Exponent Bi-exponent Bell Shaped

specifies the grading scheme (see “Specifying the

Grading Scheme,” above).



Invert converts currently specified grading-scheme lengths or

ratios into their reciprocal values. For example, if you

specify Successive Ratio grading with a First Ratio of 2.5, the Invert command button converts the First Ratio to 0.4. That is,

4.05.2

1= .

�� Double sided specifies that all specified edges are graded according

to a double-sided scheme. (NOTE: This option is not

available for the Last Length, Exponent, Bi-exponent, or Bell Shaped schemes.)

Grading Parameters

The middle section of the Mesh Edges form contains slide bars that allow you

to specify grading parameters. GAMBIT displays only those slide bars that are

applicable to the currently specified grading scheme. The following subsec-

tions describe the parameters associated with the slide bars for each of the five

grading types. For a detailed description of the parameters associated with

each type of grading, see “Grading Scheme Input Parameters,” above.

Successive-Ratio Parameters

Ratio –��– (single-sided) specifies the ratio of successive interval

lengths (R) along all specified edges.

Ratio 1 –��– (double-sided) specifies the ratio of successive interval

lengths (R) along the segments of all specified edges

nearest to their respective start vertices.

Ratio 2 –��– (double-sided) specifies the value of R along the seg-

ments of all specified edges nearest to their respective

end vertices.



First-Length Parameters

Length –��– (single-sided) specifies the length of the first interval on

all specified edges ( 1l ).

Length 1 –��– (double-sided) specifies the length of the first interval

on the segments of the specified edges nearest to their

respective start vertices ( 1,1l ).

Length 2 –��– (double-sided) specifies the length of the first interval

on the segments of the edges nearest to their respective

end vertices ( 2,1l ).

Last-Length Parameters

Length –��– specifies the length of the last interval on all specified

edges ( nl ).

First-Last Ratio Parameters

Ratio –��– (single-sided) specifies the ratio of the first interval

length to the last interval length on the specified edges

( nll1 ).

Ratio 1 –��– (double-sided) specifies the ratio of the first interval

length to the last interval length on the segments of the

specified edges nearest to their respective start vertices

( 1,1,1 nll ′ ).

Ratio 2 –��– (double-sided) specifies the ratio of the first interval

length to the last interval length on the segments of the

specified edges nearest to their respective end vertices

( 2,2,1 nll ′ ).



Last-First Ratio Parameters

Ratio –��– (single-sided) specifies the ratio of the last interval

length to the first interval length on the specified edges

( 1lln ).

Ratio 1 –��– (double-sided) specifies the ratio of the last interval

length to the first interval length on the segments of the

specified edges nearest to their respective start vertices

( 1,11, lln′ ).

Ratio 2 –��– (double-sided) specifies the ratio of the last interval

length to the first interval length on the segments of the

specified edges nearest to their respective end vertices

( 2,12, lln′ ).

Exponent Parameter

Ratio –��– specifies the input parameter, x, that determines the

ratio (R) of successive interval lengths for the Exponent grading scheme (see above).

Bi-exponent Parameter


ratio (R) of successive interval lengths for the Bi-exponent grading scheme (see above).

Bell Shaped Parameter


shape of the mesh node distribution for the Bell Shaped grading scheme.



Mesh Node Spacing Parameters

Spacing —————————————————————————

�� Apply specifies that the currently displayed spacing parameters

are applied to all specified edges.

Default resets mesh node spacing specifications to their default

values.

Interval size �� Interval count Shortest edge (%)

specifies the method used to determine the total number of

mesh nodes on any edge. The three available methods are

as follows:

• Interval size—specifies the size of intervals (constant

ratio grading only)

• Interval count—specifies the number of intervals

along the edge

• Shortest edge (%)—specifies that the interval size

represents a percentage of the length of the shortest

edge in the list of specified edges

Value specifies a numerical value associated with the method

used to determine the total number of intervals on any

edge.

Grading and Meshing Options

Options —————————————————————————

�� Mesh specifies that the edges are to be meshed. If you do not

specify the Mesh option, GAMBIT grades but does not

create mesh nodes on the edges.

�� Remove old mesh

specifies that any existing mesh nodes and/or elements are

removed from the edges.

�� Ignore size functions

specifies that GAMBIT ignores any existing size-function

specifications that would otherwise affect the edge mesh.



3.2.2 Set Edge Element Type

The Set Edge Element Type operation (default set command for the

MESH.NODES.EDGE default variable) specifies the number of edge nodes

upon which all face and volume meshes are based.

The edge element type determines the number of edge mesh nodes corre-

sponding to face and volume elements in the model. There are two edge

element type options:

• 2 node

• 3 node

When you specify the 2 node option, GAMBIT creates meshes such that every

edge node constitutes one endpoint of an mesh edge element and, therefore,

one corner of a mesh face or volume element. When you specify the 3 node option, GAMBIT creates an additional mesh node in the center of each edge

mesh element. As a result, only two out of every three edge mesh nodes con-

stitute corners of mesh face or volume elements.

Figure 3-26 shows the effect of edge element type on quadrilateral face mesh

elements. In Figure 3-26(a), the edge element type is specified as 2 node, therefore, each edge mesh node constitutes one corner of a face element. In

Figure 3-26(b), the edge element type is specified as 3 node, therefore, only two out of every three edge mesh nodes constitute corners of face elements.



(a) 2 node (b) 3 node

Face mesh elements

Edges

Figure 3-26: 2 node and 3 node edge element types

The Effect on Face and Volume Element Types

When you change the edge element type specification, GAMBIT automati-

cally changes all corresponding face and volume element types. Likewise,

when you change the face or volume element types, GAMBIT automatically

changes the edge element type. The following table summarizes the general

correspondence between GAMBIT edge, face, and volume element types.

Edge Face Volume

Nodes Shape Nodes Shape Nodes

2 Triangle

Quadrilateral

3

4

Tetrahedral

Hexahedral

Wedge

Pyramid

4

8

6

5

3 Triangle

Quadrilateral

6

9

Hexahedral

Tetrahedral

Wedge

Pyramid

27

10

18

13



For a description of the face and volume element types listed above, see “Set

Face Element Type” and “Set Volume Element Type,” below.

Using the Set Edge Element Type Form

To open the Set Edge Element Type form (see below), click the Set Edge Element Type command button on the Mesh/Edge subpad.

The Set Edge Element Type form contains the following options.

�� 2 node specifies that the mesh is based on two-node edge mesh

elements.

�� 3 node specifies that the mesh is based on three-node edge mesh

elements.



3.2.3 Link/Unlink Edge Meshes

The Link/Unlink Edge Meshes command button allows you to perform the fol-

lowing operations.


Link Edge Meshes Creates hard links between edges

Unlink Edge Meshes Deletes hard links between edges

The following sections describe the procedures and specifications required to

execute the operations listed above.



Link Edge Meshes

The Link Edge Meshes operation (edge link command) creates a hard link

between edges. When you create hard links between edges in a set, GAMBIT

associates the edges with each other such that any meshing or splitting

operation applied to one or more of the edges is similarly applied to all edges

in the set.

� NOTE: When you select an edge for the Link Edge Meshes operation, GAM-

BIT automatically highlights the graphic display of any edges to which the

edge is currently linked.

Linking Edge Endpoint Vertices

When you hard-link a set of edges, GAMBIT automatically creates hard links

between the endpoint vertices of the edges. The links are created such that the

start endpoint vertices of all edges in the set are hard-linked to each other, and

the end endpoint vertices of all edges in the set are hard-linked to each other.

GAMBIT does not allow you to hard-link two edges if their endpoint vertices

are already linked to each other by means of an existing hard link. For

example, consider the set of connected edges shown in Figure 3-27.

edge.1 edge.4

Link 1

edge.2

edge.3

Link 2

vertex.2 vertex.3

vertex.4vertex.1

Figure 3-27: Edge hard-link restriction—example



If you create a hard link between edge.1 and edge.4 (Link 1), GAMBIT does

not allow you to also create a hard link between edge.2 and edge.3 (Link 2), because vertex.1 and vertex.2 are already linked to vertex. 3 and vertex.4, respec-tively.

Reversing the Grading Orientation

When you select an edge for hard-linking, GAMBIT allows you to reverse the

orientation of grading on the edge relative to its start and end endpoint

vertices. To reverse the grading orientation of an edge, Shift-middle-click the

edge in the graphics window when selecting it for hard-linking. (NOTE: If

you reverse the grading orientation, GAMBIT does not change the sense of

the edge.)

As an example of the effect of reversing the grading orientation, consider the

two hard-linked edges shown in Figure 3-28, one of which is meshed using a

successive-ratio grading scheme with a first ratio of 2.

edge.1

Mesh nodes

a) Without reverse orientation

edge.2

edge.1

b) With reverse orientation

edge.2

Start vertices

End vertices

Figure 3-28: Linked edge meshes—effect of reverse orientation

If you do not reverse the grading orientation of either edge, the grading

scheme for edge.1 is exactly duplicated on edge.2 (see Figure 3-28(a)). If you do reverse the grading orientation, the grading scheme on edge.2 is exactly reversed relative to that of edge.1 (see Figure 3-28(b)).



Specifying the Periodic Option

The Link Edge Meshes command includes a Periodic option that allows you to specify that the edges are periodically linked. Periodically linked edges are

constrained such that they must behave identically to each other with respect

to any virtual edge-split and vertex-move operations.

As an example of the effect of periodic linking, consider the square, planar

face shown in Figure 3-29, two edges (edge.1 and edge.3) of which are hard-linked to each other.

(a) (b)

edge.1 edge.3

v_vertex.5 v_vertex.6Split point

v_edge.5 v_edge.7

v_edge.8v_edge.6

Linked edges

Figure 3-29: Virtual splitting of two hard linked edges

If you perform a virtual split of edge.1 at the split point shown in Figure 3-29(a), GAMBIT splits both edges to create the geometric entities shown in

Figure 3-29(b). (NOTE: In this example, the hard link was created such that

the grading orientations of edge.1 and edge.3 point in the same direction,

therefore v_edge.5 and v_edge.7 are equal in length. If the grading orientations had opposed each other when the link was created, v_edge.8 would be equal in length to v_edge.5, and v_edge.7 would be equal in length to v_edge.6).



If you move v_vertex.5 in Figure 3-29 by means of the Slide Virtual Vertex command (see Section 2.2.2), the final state of v_vertex.6 depends on two factors:

• The state of the Move with links option on the Slide Virtual Vertex form

• Whether or not the link between edge.1 and edge.3 is Periodic

Specifically, the rules governing the vertex move can be summarized as

follows (see Figure 3-30):

Periodic link Move with links option Move v_vertex.6 Figure 3-30

Yes On Yes (a)

Yes Off Yes (a)

No On Yes (a)

No Off No (b)

For example, if edge.1 and edge.3 are periodically linked, GAMBIT moves

v_vertex.6 regardless of the state of the Move with links option. Likewise, if you specify the Move with links option, GAMBIT moves v_vertex.6 regardless of whether the link between edge.1 and edge.3 is periodic.



(b) v_vertex.6 unmoved

v_vertex.5

v_vertex.6

(a) v_vertex.6 moved

v_vertex.5 v_vertex.6

Figure 3-30: v_vertex.6 move states—Periodic and Move with links options

Using the Link Edge Meshes Form

To open the Link Edge Meshes form (see below), click the Link command


The Link Edge Meshes form contains the following specifications.

Edges � specifies the edges to be hard-linked.

�� Periodic specifies that the edges are to be periodically linked.



Unlink Edge Meshes

The Unlink Edge Meshes operation (edge unlink command) deletes existing

hard links associated with one or more edges. When you unlink an edge,

GAMBIT deletes the link(s) between the specified edge and the edge to which

it is hard-linked.

� NOTE: When you select an edge for the Unlink Edge Meshes operation, GAM-

BIT automatically highlights the graphics window display of any edges to

which the edge is currently linked.

Using the Unlink Edge Meshes Form

To open the Unlink Edge Meshes form (see below), click the Unlink command


The Unlink Edge Meshes form contains the following specifications.

Edge � specifies the edge(s) for which the hard link is to be deleted.

�� Lower topology specifies that all vertex hard links that are associated with the

specified edge are deleted along with the corresponding edge

hard links.



3.2.4 Split Meshed Edge

The Split Meshed Edge operation (edge split meshnode command) splits

a real or virtual edge at a mesh node.

When you split an edge at a mesh node, GAMBIT splits the edge into two

virtual edges that share a common virtual endpoint vertex. The common ver-

tex is located at the position of the specified node.

When you specify the edge to be split, GAMBIT displays its existing mesh in

the graphics window. To specify the exact mesh node at which the edge is to

be split, either pick the node in the graphics window (using the mouse) or

select the mesh node by means of the Mesh Node pick-list form.

Using the Split Meshed Edge Form

To open the Split Meshed Edge form (see below), click the Split Edge com-

mand button on the Mesh/Edge subpad.

The Split Meshed Edge form contains the following specifications.

Edge � specifies the edge to be split.

Split With —————————————————————————

Node specifies the node at which the edge is to be split.



3.2.5 Summarize Edge Mesh

The Summarize Edge Mesh operation (edge msummarize command) dis-

plays edge mesh information in the Transcript window and allows you to highlight specific mesh nodes and/or edge mesh elements in the graphics

window. The command requires three input parameters:

• Edge for which the mesh is to be summarized

• Type of component (elements or nodes) to be summarized

• Specific components to be included in the summary

Specifying the Component Type

To summarize edge mesh information in the Transcript window, you must

specify the type of mesh components to be included in the summary. Each

edge mesh includes two component types:

• Elements

• Nodes

The type of edge mesh summary information displayed in the Transcript window depends on the component type (see “Edge Mesh Summary

Information,” below).

Selecting Specific Components

GAMBIT provides two methods for selecting specific components (elements

or nodes) to be included in the edge mesh summary:

• Picking the components in the graphics window

• Selecting the components by means of a pick list

In most cases, it is preferable to pick the components in the graphics window,

rather than selecting them by means of a pick list, because the component

labels (element or node numbers) are not known prior to component selection.

To pick the components in the graphics window:

1. Select the appropriate Component option (Elements or Nodes).

2. Click (to activate) the appropriate (Elements or Nodes) pick-list field.

3. Shift-left-click in the graphics window to select each element or node

to be included in the summary.



To select the components by means of a pick list:


2. Click the appropriate (Elements or Nodes) pick-list button to open the Mesh Edge List (Multiple) or Mesh Node List (Multiple) form.

3. On the Mesh Edge List (Multiple) or Mesh Node List (Multiple) form,

click the All–> pushbutton to populate the list with all elements or

nodes associated with the specified edge.

4. In the Mesh Edge List (Multiple) or Mesh Node List (Multiple) list, select (highlight) the elements or nodes to be excluded from the summary.

5. Click the <– – – pushbutton to remove the selected (highlighted) ele-

ments or nodes from the list.

� NOTE: The Mesh Edge List (Multiple) and Mesh Node List (Multiple) forms do

not include the Available list field that is included on most pick-list forms

because of the number of items that might need to be included in the list field.

A fully meshed model can contain tens of thousands of edge mesh elements or

nodes, each of which constitutes an Available component. If the Mesh Edge List (Multiple) or Mesh Node List (Multiple) form included an Available list field, GAMBIT would need to compile the Available list before opening the form,

thereby delaying the appearance of the form on the GUI.

When you specify any component (element or node) to be included in the

edge mesh summary, GAMBIT highlights the component in the graphics

window. If you select the Element labels and/or Node labels options, GAMBIT

also displays the element and/or node numbers associated with the specified

components (see Figure 3-31).



Node

numbers

Element

numbers

Figure 3-31: Edge mesh element and node numbering display

Edge Mesh Summary Information

As noted above, the type of edge mesh summary information displayed in the

Transcript window depends on the type of component being summarized. For

example, element summaries include node connectivity information, which is

not available in node summaries.

Elements Summary Information

If you select the Elements option, the edge mesh summary includes the fol-

lowing information for each specified element.

• Element number

• Element type

• Number (count) of nodes associated with the element

• Connectivity of nodes associated with the element

� NOTE: For edge mesh summary information, the element type is always

“edge” and the number (count) of nodes associated with each element is

always “2”.



For example, if you select an Elements summary for the edge and highlighted

elements shown in Figure 3-31, above, GAMBIT displays the following infor-

mation in the Transcript window.

Total nodes: 6

Total elements: 3

Element Type Count Connectivity

----------- --------- -------------- ----------------------

1 edge 2: 1 3

3 edge 2: 4 5

4 edge 2: 5 6

In this case, the summary indicates that element 3 is an edge mesh element

connected to nodes 4 and 5.

Nodes Summary Information

If you select the Nodes option, the edge mesh summary includes the following

information for each specified node.

• Node number

• Coordinates (x, y, z) of the node

• Geometric entity (“owner”) associated with the node

For example, if you select a Nodes summary for the edge and highlighted

nodes shown in Figure 3-31, above, GAMBIT displays the following informa-

tion in the Transcript window.

Total nodes: 6

Total elements: 3

Coordinate System: c_sys.1

Node x y z Owner

----------- --------- ---------- --------- -------------

1 5.0000 5.0000 -5.0000 vertex.4

3 5.0000 3.0000 -5.0000 edge.3

4 5.0000 1.0000 -5.0000 edge.3

5 5.0000 -1.0000 -5.0000 edge.3

6 5.0000 3.0000 -5.0000 edge.3

In this case, the summary indicates that node 1 is located at the position (5, 5,

-5) and is associated with (“owned by”) vertex.4.



Using the Summarize Edge Mesh Form

To open the Summarize Edge Mesh form (see below), click the Summarize command button on the Mesh/Edge subpad.

The Summarize Edge Mesh form contains the following options and specifica-

tions.

Edge � specifies the edge for which summary information is to be

displayed.

Component —————————————————————————

�� Elements displays summary information for specified elements.

All � Pick

specifies whether the mesh summary information

includes all elements or only selected elements.

Pick � specifies the elements for which mesh summary

information is to be displayed.

�� Element labels displays labels (numbers) in the graphics window for all

specified elements.

�� Node labels displays labels (numbers) in the graphics window for all

nodes associated with the specified elements.

�� Nodes displays summary information for specified nodes.

All � Pick

specifies whether the edge mesh summary information

includes all nodes or only selected nodes.



Pick � specifies the nodes for which edge mesh summary



specified nodes.



3.2.6 Delete Edge Meshes

The Delete Edge Meshes operation (edge delete onlymesh command)

deletes the mesh (and, optionally, mesh grading information) on one or more

edges.

Using the Delete Edge Meshes Form

To open the Delete Edge Meshes form (see below), click the Delete command


The Delete Edge Meshes form contains the following specifications.

Edges � specifies the edge(s) from which the mesh is to be deleted.

All � Pick

• All specifies all edges in the model.

• Pick specifies edges selected by means of the Edges list box.

�� Reset to default values

resets the grading parameters associated with the specified

edge(s) to their default values.

Face Meshing Commands MESHING THE MODEL


3.3 Face Meshing Commands

The following commands are available on the Mesh/Face subpad.


Mesh Faces Creates mesh nodes on faces

Move Face Nodes Split Quad Meshes

Adjusts mesh node positions on a

face; splits quadrilateral face mesh

elements into triangular elements

Smooth Face Meshes Adjusts face mesh node positions to

improve uniformity of node spacing

Set Face Vertex Type Specifies the characteristics of a face

mesh in the vicinity of a corner

Set Face Element Type Specifies face element types used


Link Face Meshes Unlink Face Meshes

Creates or removes mesh hard links

between faces

Modify Meshed Face Split Meshed Face

Converts mesh edges to topological

equivalents; splits faces along

boundaries defined by mesh node

locations

Summarize Face Mesh Check Face Meshes

Displays mesh information in the

graphics window; summarizes face

mesh quality information

Delete Face Meshes Deletes existing mesh nodes and/or

elements from faces

MESHING THE MODEL Face Meshing Commands


3.3.1 Mesh Faces

The Mesh Faces operation (face mesh and face modify commands)

creates the mesh for one or more faces in the model. When you mesh a face,

GAMBIT creates mesh nodes on the face according to the currently specified

meshing parameters.

The Mesh Faces operation requires the following input parameters:

• Face(s) to be meshed

• Meshing scheme

• Mesh node spacing

• Face meshing options

Specifying the Faces

GAMBIT allows you to specify any face for a meshing operation; however,

the shape and topological characteristics of the face, as well as the vertex

types associated with the face, determine the type(s) of mesh scheme(s) that

can be applied to the face.

Specifying the Meshing Scheme

To specify the face-meshing scheme, you must specify the following para-

meters:

• Elements

• Type

• Smoother (Map meshes only)

The Elements parameter defines the shape(s) of the elements that are used to

mesh the face. The Type parameter defines the pattern of mesh elements on

the face. The Smoother specification determines the type of smoothing algo-

rithm (if any) used to smooth a mapped mesh during the meshing operation.

The following sections describe the parameters listed above and their effects

on the overall face mesh.



Specifying Scheme Elements

GAMBIT allows you to specify any of the following face meshing Elements options.

Option Description

Quad Specifies that the mesh includes only quadrilateral mesh

elements

Tri Specifies that the mesh includes only triangular mesh

elements

Quad/Tri Specifies that the mesh is composed primarily of quadrilat-

eral mesh elements but includes triangular corner elements at

user-specified locations (see “Set Face Vertex Type,” below)

Each of the Elements options listed above is associated with a specific set of Type options (see below).

Specifying Scheme Type

GAMBIT provides the following face meshing Type options.

Option Description

Map Creates a regular, structured grid of mesh elements

Submap Divides an unmappable face into mappable regions

and creates structured grids of mesh elements in each

region

Pave Creates an unstructured grid of mesh elements

Tri Primitive Divides a three-sided face into three quadrilateral

regions and creates a mapped mesh in each region

Map Split Creates a mapped mesh of quadrilateral elements and

splits the elements to create triangular elements

Submap Split Creates a submapped mesh of quadrilateral elements

and splits the elements to create triangular elements

Wedge Primitive Creates triangular elements at the tip of a wedge-

shaped face and creates a radial mesh outward from

the tip



As noted above, each of the Elements options is associated with a specific set of one or more of the Type options listed above. The following table shows the correspondence between each of the face meshing Elements and Type options. (NOTE: Shaded cells marked with an “X” represent allowable combi-

nations of options.)

Elements

Type Quad Tri Quad/Tri

Map ×××× ××××

Submap ××××

Pave ×××× ×××× ××××

Tri Primitive ××××

Map Split ××××

Submap Split ××××

Wedge Primitive ××××

Each of the allowable combinations shown in the table above results in a spe-

cific pattern of mesh nodes for any given face. In addition, each is associated

with a set of restrictions that govern when it can or cannot be applied. The

following sections describe the patterns and restrictions associated with each

of the allowable combinations of Elements and Type options listed above.

� NOTE: When you specify a face on the Mesh Faces form, GAMBIT auto-

matically evaluates the face with respect to its shape, topological characteris-

tics, and vertex types and sets the Scheme option buttons to reflect a recom-

mended face meshing scheme. If you specify more than one face for a mesh-

ing operation, the scheme represented by the Scheme option buttons reflects the recommended scheme for the most recently specified face. You can

enforce a meshing scheme, and thereby override any recommended scheme,

by means of the Scheme option buttons on the Mesh Faces form. When you

enforce a meshing scheme, GAMBIT applies the specified scheme to all cur-

rently picked faces.



Quad:Map Meshing Scheme

When you apply the Quad:Map meshing scheme to a face, GAMBIT meshes

the face using a regular grid of quadrilateral face mesh elements, such as those

shown in Figure 3-32.

Figure 3-32: Quad:Map face meshing scheme—example mesh

The Quad:Map meshing scheme is applicable primarily to faces that are

bounded by four or more edges, however not all such faces are suitable for

mapping. To be “mappable,” a face must not violate restrictions related to the

following parameters:

• Vertex types

• Edge mesh intervals

The vertex-type and edge mesh interval restrictions for the Quad:Map meshing

scheme are as follows.



Vertex Types

To be mappable, a face must represent a logical rectangle. (For the exception

to this criterion, see NOTE (1), below.) To represent a logical rectangle, a face

must include four End type vertices, and all other vertices associated with the face must be designated as Side type vertices.

Figure 3-33 shows four planar faces, two of which are mappable and two of

which are not mappable. The faces shown in Figure 3-33(a) and (c) are map-

pable, because each includes four End type vertices and all other vertices asso-ciated with the face are Side type vertices. The face shown in Figure 3-33(b) is not mappable, because it includes only three End type vertices. The face shown in Figure 3-33(d) is not mappable, because one of its vertices is desig-

nated as a Reversal type vertex.

End

End

End

End

(a) Mappable

End

End

Side

EndSide

(b) Not mappable

End

End

End

End

Side

Side

Side

End

End

End

End

Side

Reversal

Side

(c) Mappable (d) Not mappable

Figure 3-33: Quad:Map face meshing scheme—face suitability

� NOTE (1): If a face is bounded by two closed-loop edges, GAMBIT can

employ the Quad:Map meshing scheme even if the vertex type designations do

not define a logical rectangle. For example, GAMBIT automatically applies

the Quad:Map meshing scheme to a cylindrical face, even though the circular

edges that bound the face possess only one vertex each and both vertices are,

by default, designated as Side type vertices. Likewise, GAMBIT can use a

Quad:Map scheme to mesh an annular face.



� NOTE (2): If you enforce a Quad:Map meshing scheme on a face, GAMBIT

evaluates the face with respect to its vertex type designations. If the vertex

types do not meet the criteria outlined above, GAMBIT attempts to change the

vertex types so that the face is rendered mappable.

If the specified face includes more than four vertices, there are multiple con-

figurations of vertex types that satisfy the vertex-type criteria. For example, if

the face includes five vertices, there are five possible vertex-type configura-

tions that allow the creation of a Quad:Map mesh, because any of the five ver-

tices can be designated as the Side vertex. When GAMBIT automatically

changes vertex types, it attempts to employ the configuration that minimizes

distortion in the mesh.

Each vertex-type configuration results in a unique node pattern for the

mapped mesh. To enforce a specific node pattern on a mapped mesh, manu-

ally specify the vertex types such that they meet the Quad:Map scheme vertex-

type criteria outlined above. (See “Set Face Vertex Type,” below.)

Edge Mesh Intervals

If you grade or mesh the edges of a face prior to creating a mapped mesh, you

must specify the edge mesh intervals such that the numbers of mesh intervals

on opposing sides of the logical rectangle are equal. For meshing purposes, a

single side of the logical rectangle consists of all edges that exist between any

two End type vertices.

� NOTE: If you do not grade or mesh the edges of a face prior to creating the

mapped mesh, GAMBIT automatically assigns edge mesh intervals such that

they satisfy the criteria described above.

As an example of the edge mesh interval restriction, consider the face shown

in Figure 3-34. The face includes four End type vertices and one Side type vertex.



End

Side

End End

Endedge.1

edge.5

edge.4

edge.3

edge.2

Figure 3-34: Mappable planar face consisting of five edges

The four sides of the logical rectangle that bounds the face can be defined as

follows.

Side Edge

1 edge.2

2 edge.3

3 edge.4

4 edge.1 and edge.5

For the face to be mappable, the number of mesh intervals on edge.2 (Side 1) must be equal to that on edge.4 (Side 3). Likewise, the combined number of

intervals on edge.1 and edge.5 (Side 4) must be equal to the number of inter-

vals on edge.3 (Side 2).



� NOTE (1): If you grade or mesh one or more edges of a face and apply a

Quad:Map meshing scheme to the face, GAMBIT automatically meshes the

remaining edges such that the numbers of intervals on opposing sides of the

face satisfy the criteria outlined above. For example, if you grade or mesh

edge.3 in Figure 3-34 such that it contains 10 intervals, GAMBIT meshes

edge.1 and edge.5 such that they include a combined total of 10 intervals.

� NOTE (2): GAMBIT does not include the edge mesh interval restriction when

evaluating a face with respect to a recommended meshing scheme. As a result,

GAMBIT may recommend a Quad:Map meshing scheme for a face that is

mappable with respect to its vertex-type configuration but which cannot be

mapped, because it violates the edge mesh interval restriction.

� NOTE (3): If you create a mesh link between two edges that constitute

opposing sides of a logical rectangle, the edges automatically satisfy the edge

mesh interval restriction described above.

� NOTE (4): If you mesh a face using the Quad:Map meshing scheme, you can

smooth the mesh during its creation by means of the Smoother options (see “Specifying Scheme Smoother Algorithm,” below).

� NOTE (5): When you apply the Quad:Map scheme to a face bounded by two

closed loops (for example, a cylindrical or annular face), GAMBIT allows you

to specify the number of mesh intervals between the loops (see “Specifying

Projection Intervals,” below).



Quad:Submap Meshing Scheme

When you apply the Quad:Submap meshing scheme to a face, GAMBIT

divides the face into one or more mappable regions and creates a mapped

mesh in each region. Like the Quad:Map meshing scheme, the Quad:Submap meshing scheme is subject to restrictions related to vertex types and edge

mesh intervals. The vertex-type and edge mesh interval restrictions for the

Quad:Submap meshing scheme are as follows.

Vertex Types

To constitute a submappable face, a face must possess only End, Side, Corner,

and Reversal vertices. In addition, the total number of End vertices, EN , must

satisfy the following equation:

RCE NNN 24 ++=

where CN and RN are the total numbers of Corner and Reversal type vertices,

respectively, on the face. That is, for every Corner type vertex, the face must

possess an additional End vertex, and for every Reversal vertex, the face must

possess two additional End vertices.

The shape of the mesh generated by means of the Quad:Submap face meshing

scheme depends on the type and arrangement of vertex types on the face. As

an example of the effect of vertex types, consider the faces shown in Figure

3-35 and Figure 3-36, each of which consists of an identical planar L-shaped

face, one corner of which is truncated at an angle.



A: End

C: Corner

G: Side

F: End E: End

D: End

B: End

H

Figure 3-35: Quad:Submap face meshing scheme—inside Corner vertex

A: End

C: Reversal

G: End

F: End E: End

D: End

B: End

H

Figure 3-36: Quad:Submap face meshing scheme—inside Reversal vertex



In Figure 3-35, the inside corner vertex I is designated as a Corner vertex, therefore, in order to be submappable, the face must possess five End type ver-tices (A, B, D, E, and F). The Quad:Submap meshing scheme divides the face

into the following two mapped regions:

• A, B, C, H, F, G

• C, D, E, H

In Figure 3-36, the inside corner vertex I is designated as a Reversal vertex, therefore, in order to be submappable, the face must possess six End type vertices (A, B, D, E, F, and G). In this case, the Quad:Submap meshing scheme

divides the face into the following two mapped regions:

• A, B, C, H, G

• C, D, E, F, H

� NOTE: If you enforce a Quad:Submap meshing scheme on a face, GAMBIT

evaluates the face with respect to its vertex type designations. If the vertex

types do not meet the criteria outlined above, GAMBIT attempts to change the

vertex types so that the face is submappable.

For most submappable faces, there are multiple configurations of vertex types

that satisfy the vertex-type criteria. Each vertex-type configuration results in a

unique node pattern for the submapped mesh. When GAMBIT automatically

changes vertex types, it attempts to employ the configuration that minimizes

distortion in the mesh. To enforce a specific node pattern on a submapped

mesh, manually specify the vertex types such that they meet the Quad:Submap scheme vertex-type criteria outlined above. (See “Set Face Vertex Type,”

below.)

Edge Mesh Intervals

If you grade or mesh the edges of a face before applying the Quad:Submap scheme, the edge mesh grading schemes must be specified such that the total

numbers of intervals on opposite sides of any given submapped region are

equal. For example, in Figure 3-35, the number of intervals (I) on each side of

the submapped regions can be expressed as follows:

20119 =+=+= DEBCAGF III

and 20119 =+=+= CDABFHE III .

Similarly, in Figure 3-36, the number of intervals (I) on each side of the sub-

mapped regions are



12== AGBCH II

and 12== EFHCD II .

� NOTE (1): If you grade or mesh one or more edges of a face before applying a

Quad:Submap meshing scheme to the face, GAMBIT automatically meshes the

remaining edges such that the numbers of intervals on opposing sides of the

face satisfy the criteria outlined above.

� NOTE (2): GAMBIT does not include the edge mesh interval restriction when

evaluating a face with respect to a recommended meshing scheme. As a result,

GAMBIT may recommend a Quad:Submap meshing scheme for a face that is

submappable with respect to its vertex-type configuration but which cannot be

submapped, because it violates the edge mesh interval restriction outlined

above.

� NOTE (3): When you apply the Quad:Submap scheme to a face bounded by

two closed loops (for example, a cylindrical or annular face), GAMBIT allows

you to specify the number of mesh intervals between the loops (see

“Specifying Projection Intervals,” below).



Quad:Pave Meshing Scheme

When you apply the Quad:Pave meshing scheme, GAMBIT creates an

unstructured face mesh consisting of quadrilateral mesh elements (see Figure

3-37).

Figure 3-37: Quad:Pave face meshing scheme—example mesh

You can apply the Quad:Pave meshing scheme to any face that consists of a

closed loop of edges.



� NOTE: The Quad:Pave meshing algorithm can sometimes fail when pre-

graded (or meshed) boundary edges possess interval lengths that vary widely

along the edges. In such cases, it is often possible to help the meshing algo-

rithm to succeed by applying a mesh-based size function to the face. (For a

description of mesh-based size functions, see “Meshed Size Functions” in

Section 5.2.2 in this guide.)

You can force GAMBIT to automatically apply mesh-based size functions

where appropriate to successfully create a Quad:Pave mesh. The specification

is made by means of two default variables:

• MESH.PAVER.CREATE_OWN_SF

• MESH.PAVER.SIZE_VARIATION_LIMIT

The CREATE_OWN_SF default variable can take on the following values:

• -1—GAMBIT evaluates each edge and automatically applies a size

function to any face the edges of which possess a wide variation in

interval lengths.

• 0—GAMBIT does not automatically apply any size functions.

• 1—GAMBIT automatically applies a size function to every face to be

meshed.

The SIZE_VARIATION_LIMIT default variable specifies the interval-length

difference that triggers the automatic application of the size functions. Its

value represents the ratio of the maximum interval length to the minimum

interval length for any pre-graded/meshed edges associated with the face(s) to

be meshed using the Quad:Pave algorithm.

Vertex Types

There are no restrictions on vertex types associated with a Quad:Pave mesh.

Edge Mesh Intervals

If you grade or mesh all of the boundary edges of a face before applying the

Quad:Pave meshing scheme, you must specify the grading such that the total

number of mesh intervals on all edges is an even number. If you grade some,

but not all, of the face boundary edges, GAMBIT automatically meshes the

remaining edges such that the total number of edge mesh intervals is even.



Quad:Tri Primitive Meshing Scheme

The Quad:Tri Primitive meshing scheme allows you to create a submapped mesh

on a three-sided face. (NOTE: Any side of the three-sided face may consist of

more than one edge.) When you apply the Quad:Tri Primitive meshing scheme to

a three-sided face, GAMBIT locates a point internal to the face that serves as

a common endpoint for three mappable subregions.

Figure 3-38 shows a triangular, planar face meshed according to the Quad:Tri Primitive meshing scheme. Note that the face is divided into three mappable

regions, each of which shares a common endpoint (D). The regions are

defined by the quadrilaterals AFDE, FBGD, and EDGC.

A: End

D

C: End

B: End

F

G

E

Figure 3-38: Quad:Tri Primitive face meshing scheme—example mesh

The vertex-type and edge mesh interval restrictions for the Quad:Tri Primitive meshing scheme are as follows.

Vertex Types

The Quad:Tri Primitive meshing scheme requires that the vertices at the corners

of the three sides of the face are specified as End vertices (see Figure 3-38, above) and that all other vertices are specified as Side vertices.



Edge Mesh Intervals

If you grade or mesh the sides of the face before applying the Quad:Tri Primitive meshing scheme, you must specify the grading such that the total number of

intervals on the three sides of the face is an even number. In addition, the

grading must satisfy the following criterion:

2+≥+ kji III

where iI and jI are the numbers of intervals on any two sides, and kI is the

number of intervals on the remaining side.



Tri:Pave Meshing Scheme

When you apply the Tri:Pave meshing scheme, GAMBIT creates a face mesh

consisting of irregular triangular mesh elements, such as that shown in Figure

3-39.

Figure 3-39: Tri:Pave face meshing scheme—example mesh

The vertex-type and edge mesh interval restrictions for the Tri:Pave meshing

scheme are as follows.

Vertex Types

There are no restrictions on vertex types associated with the Tri:Pave meshing

scheme.

Edge Mesh Intervals

There are no restrictions on the edge mesh intervals for the Tri:Pave meshing

scheme.



Tri:Map Split Meshing Scheme

When you apply the Tri:Map Split meshing scheme, GAMBIT creates a

Quad:Map mesh and splits the resulting quad elements diagonally to create a

triangular mesh. For example, if you mesh a simple square face using the

Tri:Map Split meshing scheme, GAMBIT creates a mesh such as that shown in

Figure 3-40.

Figure 3-40: Tri:Map Split face meshing scheme

Any face to be meshed using the Tri:Map Split scheme must meet the mappabil-

ity requirements that apply to the Quad:Map meshing scheme (see “Quad:Map

Meshing Scheme,” above). If the specified face does not meet the Quad:Map requirements, GAMBIT attempts to use a Tri:Submap Split scheme to mesh the

face (see “Tri:Submap Split Meshing Scheme,” below).

Excluding Boundary Layers

When you select the Tri:Map Split meshing scheme, GAMBIT activates the

Exclude boundary layer faces option, which allows you to specify whether GAMBIT splits boundary layer elements when splitting the mesh. Figure 3-41

shows the effect of the Exclude boundary layer faces option on a simple square

face with a fixed boundary layer attached to one side.



(a) Exclude boundary layer faces on (b) Exclude boundary layer faces off

Figure 3-41: Tri:Map Split—effect of Exclude boundary layer faces option

Vertex Types

Vertex type restrictions for the Tri:Map Split meshing scheme are identical to

those for the Quad:Map mesh scheme (see “Quad:Map Meshing Scheme,”

above). If the vertex types do not exactly meet the Quad:Map vertex type criteria, GAMBIT attempts to change vertex types where necessary to create

the mapped mesh and execute the Tri:Map Split operation.

Edge Mesh Intervals

Edge mesh interval restrictions for the Tri:Map Split meshing scheme are identi-

cal to those for the Quad:Map mesh scheme (see “Quad:Map Meshing

Scheme,” above).



Tri:Submap Split Meshing Scheme

When you apply the Tri:Submap Split meshing scheme, GAMBIT creates a

Quad:Submap mesh and splits the resulting quad elements diagonally to create

a triangular mesh. For example, Figure 3-42 shows the results of the

Tri:Submap Split scheme for a simple L-shaped face.

Figure 3-42: Tri:Submap Split face meshing scheme

Any face to be meshed using the Tri:Submap Split scheme must meet the map-

pability requirements that apply to the Quad:Submap meshing scheme (see

“Quad:Submap Meshing Scheme,” above).

Excluding Boundary Layers

When you select the Tri:Submap Split meshing scheme, GAMBIT activates the

Exclude boundary layer faces option, which allows you to specify whether GAMBIT splits boundary layer elements when splitting the mesh. Figure 3-43

shows the effect of the Exclude boundary layer faces option on the face shown in Figure 3-42, above, with a fixed boundary layer attached to one side.



(a) Exclude boundary layer faces on (b) Exclude boundary layer faces off

Figure 3-43: Tri:Submap Split—effect of Exclude boundary layer faces option

Vertex Types

Vertex type restrictions for the Tri:Submap Split meshing scheme are identical

to those for the Quad:Submap mesh scheme (see “Quad:Submap Meshing

Scheme,” above). If the vertex types do not exactly meet the Quad:Submap vertex type criteria, GAMBIT attempts to change vertex types where neces-

sary to create the submapped mesh and execute the Tri:Submap Split operation.

Edge Mesh Intervals

Edge mesh interval restrictions for the Tri:Submap Split meshing scheme are

identical to those for the Quad:Submap mesh scheme (see “Quad:Submap

Meshing Scheme,” above).



Quad/Tri:Map Meshing Scheme

The Quad/Tri:Map meshing scheme is applicable only to geometry that consti-

tutes a narrow, logical sliver consisting of two sides—such as that shown in

Figure 3-44. Either side may consist of more than one edge.

Trielement

edge.2

Trielement

edge.1

Figure 3-44: Quad/Tri:Map face meshing scheme—example mesh

When you apply the Quad/Tri:Map meshing scheme, GAMBIT creates triangu-

lar mesh elements at the two endpoints of the sides and creates quadrilateral

elements across the rest of the face. The vertex-type and edge mesh interval

restrictions for the Quad/Tri:Map meshing scheme are as follows.

Vertex Types

To employ the Quad/Tri:Map meshing scheme to a sliver-shaped face, you must

specify the vertices as follows:

• Tips of the sliver—Trielement

• All other vertices—Side

Edge Mesh Intervals

If you grade or mesh the edges that comprise the sides of a sliver-shaped face

before applying the Quad/Tri:Map meshing scheme, you must specify the edge

grading such that the sides possess identical numbers of intervals.



Quad/Tri:Pave Meshing Scheme

When you apply the Quad/Tri:Pave meshing scheme to a face, GAMBIT

creates a paved mesh that consists primarily of quadrilateral elements but

employs triangular mesh elements in any corners the edges of which form a

very small angle with respect to each other. You can also impose the creation

of triangular mesh elements in corners of the face by setting the associated

vertices as Trielement vertices. Figure 3-45 shows a Quad/Tri:Pave mesh in

which vertices A, D, and E are set as Trielement vertices.

A: Trielement

B: Corner

E: Trielement D: Trielement

C: End

F: Side

Figure 3-45: Quad/Tri:Pave face meshing scheme—example mesh

The vertex-type and edge mesh interval restrictions for the Quad/Tri:Pave meshing scheme are as follows.



Vertex Types

There are no restrictions on vertex types associated with the Quad/Tri:Pave meshing scheme, however, you can enforce the creation of either triangular or

quadrilateral corner elements by means of the Trielement or Notrielement vertex types, respectively, as follows:

• If you specify a vertex as a Notrielement vertex, GAMBIT creates a

quadrilateral element at the vertex location regardless of the angle

between its associated edges.

• If you specify a vertex as a Trielement vertex, GAMBIT creates a trian-

gular element at the vertex location regardless of the angle between its

associated edges.

Edge Mesh Intervals

If you grade or mesh all of the edges that comprise the boundary of a face

before applying the Quad/Tri:Pave meshing scheme, you must specify the grad-

ing such that

TT NIN −=

is an even number, where TI is the total number of mesh intervals on all

edges, and TN is the total number of triangle mesh elements. If you grade

some, but not all, of the edges, GAMBIT automatically meshes the ungraded

edges such that N is an even number.



Quad/Tri:Wedge Primitive Meshing Scheme

The Quad/Tri:Wedge Primitive meshing scheme allows you to create a radial

mesh on a three-sided face. (NOTE: Any side of the three-sided face may con-

sist of more than one edge.) When you apply the Quad/Tri:Wedge Primitive meshing scheme, GAMBIT creates a mapped mesh that includes a group of

triangular mesh elements emanating from common endpoint (see Figure

3-46).

B: End

A: Trielement

C: End

Figure 3-46: Quad/Tri:Wedge Primitive face meshing scheme—example mesh

The vertex-type and edge mesh interval restrictions for the Quad/Tri:Wedge Primitive meshing scheme are as follows.

Vertex Types

The Quad/Tri:Wedge Primitive meshing scheme requires that the vertices at the

corners of the three sides of the face are specified as End vertices (see Figure 3-47) and that all other vertices are specified as Side vertices.



C: End

A: Trielement

E: End

B: Side

D: Side

Figure 3-47: Quad/Tri:Wedge Primitive face meshing scheme—vertex-types

Face meshes created by means of the Quad/Tri:Wedge Primitive mesh scheme

consist of regular quadrilateral mesh elements and a group of triangular mesh

elements that share a common endpoint. The group of triangular elements

exists at the Trielement type vertex. To create the mesh, GAMBIT constructs a

series of mesh grid lines that emanate from the Trielement type vertex to the opposite side of the logical triangle—that is, to the edges that exist between

the two End type vertices (see Figure 3-47, above).

Edge Mesh Intervals

If you grade or mesh the face boundary edges before applying the

Quad/Tri:Wedge Primitive meshing scheme, you must specify the grading such

that the total numbers of intervals on opposite sides of the logical triangle are

equal. For meshing purposes, the opposite sides of the logical triangle are

defined as all edges that exist between the Trielement type vertex and each End type vertex. For example, in Figure 3-47, the combined numbers of edge mesh

intervals on the edges AB and BC must equal the total number of intervals on

edge AE.



Specifying Scheme Smoother Algorithm

If you mesh a face with Quad element types using a Map meshing scheme,

GAMBIT allows you to automatically smooth the mesh during meshing by

means of Smoother options on the Mesh Faces form. (NOTE: You can also

smooth any existing face mesh by means of the Smooth Face Meshes com-

mand (see Section 3.3.3, below).)

GAMBIT provides the following Smoother options for faces.

Option Algorithm

None No smoother applied during meshing

Thom-Mid Thomas-Middlecoff

The Thom-Mid option is useful when mesh nodes on the face boundary edges

are bunched together in certain sections of the edges. Such bunching can

affect the smoothness of the interior face mesh. The algorithm tends to smooth

the face mesh only (or primarily) in those regions affected by the bunched

edge nodes.

� NOTE: The Thom-Mid option applies only to planar faces. If you specify the Thom-Mid option when meshing a non-planar face, GAMBIT meshes the face

without smoothing and displays a warning message in the Transcript window.



Specifying Node Spacing

When you specify mesh node spacing on the Mesh Faces form, GAMBIT

applies the specification to all edges associated with any specified faces that

are not currently graded or meshed. GAMBIT provides three different ways to

specify the number of intervals on the edges of a face.

• Interval count

• Interval size

• Shortest edge (%)

For a description of the three edge mesh interval spacing options listed above,

see “Specifying Node Spacing” in Section 3.2.1.

Specifying Projection Intervals

When you apply a Quad:Map or Quad:Submap scheme to a face that is bounded

by two closed-loop edges, such as a cylindrical or annular face, GAMBIT

allows you to specify the number of “projection” intervals between the bound-

ing edges. The number of intervals is specified by means of the Proj Intervals text field on the Mesh Faces form.

As an example of the effect of the Proj Intervals value, consider the two faces shown in Figure 3-48. The cylindrical face (Figure 3-48(a)) has a height of 10

and a constant radius of 4. The annular face (Figure 3-48(b)) has inner and

outer radii of 2 and 6, respectively.



(a) Cylindrical face (b) Annular face

Figure 3-48: Faces bounded by closed-loop edges

Figure 3-49 shows the effect of the Proj Intervals value on Quad:Map meshes

for the two faces shown in Figure 3-48 when the Interval size is specified as 1. The meshes shown in Figure 3-49(a) and (b) represent Proj Intervals values of 10 and 20, respectively. The meshes shown in Figure 3-49(c) and (d) repre-

sent Proj Intervals values of 5 and 10, respectively.



(a) Proj Intervals = 10 (b) Proj Intervals = 20

(c) Proj Intervals = 5 (d) Proj Intervals = 10

Figure 3-49: Effect of Proj Intervals value

Specifying Face Meshing Options

GAMBIT includes the following primary options on the Mesh Faces form:

• Mesh

• Remove old mesh

• Remove lower mesh


Mesh Option

If you select the Mesh option, GAMBIT meshes the picked face(s) according

to the parameters as currently specified on the Mesh Faces form. If you Apply the meshing specifications without selecting the Mesh option, GAMBIT

applies the currently specified mesh parameters to the face(s) but does not

create the mesh.



Remove old mesh Option

If you select the Remove old mesh option, GAMBIT removes any currently

existing mesh from the specified face(s) before creating the new face

mesh(es). GAMBIT also enables the Remove lower mesh option (see below), which specifies whether or not to remove the mesh on pre-meshed boundary

edges. If you do not select the Remove lower mesh option, GAMBIT retains

any existing pre-assigned edge mesh(es) when meshing the face.

Remove lower mesh Option

As noted above, when you select the Remove old mesh option, GAMBIT

enables the Remove lower mesh option, which allows you to specify whether or not to remove the mesh on pre-meshed boundary edges—that is, edges for

which mesh intervals and grading specifications are assigned (using the Mesh Edges command) prior to meshing the face.

• If you select the Remove lower mesh option, GAMBIT removes any

pre-assigned edge-mesh interval assignments but retains pre-assigned

edge-mesh grading specifications.

• If you do not select the Remove lower mesh option, GAMBIT retains all

pre-assigned edge-mesh interval and grading assignments.

Ignore size functions Option


size function specifications that would otherwise affect the face mesh.



Using the Mesh Faces Form

To open the Mesh Faces form (see below), click the Mesh command button on

the Mesh/Face subpad.

The Mesh Faces form contains the following specifications.

Faces � specifies the faces to be meshed.

Scheme: —————————————————————————

�� Apply specifies that the meshing scheme indicated on the option

button is applied to all currently picked faces.

Default resets the meshing scheme option button to its default algo-

rithm value (Undetermined).

Elements: ————————————————————————

Quad � Tri Quad/Tri

specifies the mesh element shape. (NOTE: Each

Elements option is associated with its own set of allow-able Type options (see “Specifying Scheme Elements,”

above).)



Type: ————————————————————————

Map � Submap Pave Tri Primitive Wedge Primitive

specifies the type of meshing scheme used to mesh the

specified face(s).

Smoother: ————————————————————————

None � Thom-Mid

specifies whether or not to smooth the face mesh while

meshing (see “Specifying Scheme Smoother

Algorithm,” above). (NOTE: This option is available

only when using Quad element types and the Map mesh-

ing scheme.)

Spacing: —————————————————————————

�� Apply specifies that the current mesh node spacing parameters are

applied to all currently picked faces.

Default resets the mesh node spacing parameters to their default

values.

Value specifies the numerical component of the mesh node spac-

ing parameters.

Interval size � Interval count Shortest edge (%)

specifies the measurement unit component of the mesh

node spacing parameters.

Proj Intervals specifies the number of projection intervals for any mapped

or submapped face bounded by two closed-loop edges (see

“Specifying Projection Intervals”).

Options —————————————————————————

�� Mesh specifies that a new mesh is created in the specified face(s).


removes any existing mesh on the specified face(s).



�� Remove lower mesh

removes pre-assigned edge-mesh interval information for

the specified face(s). (NOTE: GAMBIT retains any pre-

assigned grading specifications.)



specifications that would otherwise affect the face mesh.



3.3.2 Move Face Nodes/Split Quad Meshes

The Move Face Nodes/Split Quad Meshes command button allows you to per-

form the following operations.


Move Face Nodes Adjusts face-element corner nodes

within the interior of a meshed face

Split Quad Meshes Splits quadrilateral face mesh

elements into triangular elements





Move Face Nodes

The Move Face Nodes operation (face move meshnodes command) reposi-

tions mesh nodes that exist in the interior of a meshed face. You can move the

mesh nodes either by means of the Move Face Nodes form or by means of the

mouse.

To move a face node, you must specify the following parameters and options:

• The meshed face upon which the nodes exist

• The number of the node to be moved

• The coordinates of the new node location

• Smooth option

The following paragraphs describe the specifications listed above as well as

the procedure required to move face mesh nodes by means of the mouse.

Specifying the Face

When you specify a face for which mesh nodes are to be moved, GAMBIT

highlights the face the graphics window and displays the corresponding mesh

as a series of grid lines. Face nodes are located at the intersections of the grid

lines.

Specifying the Node Number

To specify a node to be moved, you must input the corresponding node num-

ber on the Move Face Nodes form. To open a complete list of available node

numbers associated with the specified face:

1. Click the Nodes pick list button.

2. Click All on the Nodes pick list form.

When you click the All command button, GAMBIT fills the Nodes pick list with the numbers of all nodes associated with the specified face and displays

the nodes on the mesh grid in the graphics window. (NOTE: The Nodes list includes only face-element corner nodes that are interior to the face.) When

you select a node number from the Nodes pick list, GAMBIT highlights the

node in the graphics window.

To move a series of nodes, select and specify the coordinates of each node in

turn. When you have selected and moved all nodes, click Apply on the Move Face Nodes form.



Specifying Node Coordinates

To specify the new coordinates of a face mesh node, you must specify the ref-

erence coordinate system and the coordinate parameters corresponding to the

new node location. You can input the coordinate parameters with respect to

either the Global or Local coordinate system. If you specify a node location

that does not lie on the specified face, GAMBIT automatically adjusts the

coordinate parameters so that the new node location lies on the face.

Using the Mouse to Move Face Nodes

To use the mouse to move face nodes:

1. Pick the face upon which the nodes are to be moved.

2. Shift-right-click in the graphics window to accept the selection.

3. Pick (Shift-left-click) the node to be moved and drag it to its new

location.

To move a series of mesh nodes, pick and drag each node in turn. When you

have finished moving all nodes, Shift-right-click the mouse in the graphics

window to accept and apply the new node positions.

Specifying the Smooth Option

If you specify the Smooth option when moving a node, GAMBIT smoothes the

entire mesh by adjusting the positions of mesh nodes other than the moved

node. If you specify the Smooth option for a face that includes a boundary layer, the effect of the smoothing operation depends on whether the node to be

moved exists inside or outside the boundary layer, as follows:

• If the specified node is outside the boundary layer, GAMBIT does not

alter the positions of any mesh nodes within the boundary layer.

• If the specified node is inside the boundary layer, GAMBIT adjusts the

other nodes within the boundary layer along straight lines and adjusts

the mesh outside the boundary layer accordingly.

As an example of the effect of the Smooth option, consider the square, meshed

face shown in Figure 3-50, which includes a six-row boundary layer on its

bottom edge.



B.L.

A

B

Figure 3-50: Square meshed face with boundary layer

Figure 3-51 and Figure 3-52 show the effects of the Smooth option when mov-

ing a single node located either outside (node A) or inside (node B) the bound-

ary layer.

• If you move node A and do not select the Smooth option, GAMBIT

does not adjust the positions of any other mesh nodes (see Figure

3-51(a)).

• If you move node A and do select the Smooth option, GAMBIT adjusts

the positions of other mesh nodes outside the boundary layer but does

not adjust the positions of nodes within the boundary layer (see Figure

3-51(b)).

• If you move node B and do not select the Smooth option, GAMBIT

does not adjust the positions of any other mesh nodes (see Figure

3-52(a)).

• If you move node B and do select the Smooth option, GAMBIT adjusts

the positions of several other mesh nodes inside the boundary layer

(along straight lines)—which, in turn, affects the mesh outside the

boundary layer (see Figure 3-52(b)).



(a) Smooth option off (b) Smooth option on

Figure 3-51: Effect of Smooth option on node move outside boundary layer

(a) Smooth option off (b) Smooth option on

Figure 3-52: Effect of Smooth option on node move inside boundary layer



Using the Move Face Nodes Form

To open the Move Face Nodes form (see below), click the Move Face Nodes command button on the Mesh/Face subpad.

The Move Face Nodes form contains the following specifications.

Face � specifies the meshed face upon which nodes are to be moved.

Nodes � specifies the node to be moved.

�� Smooth specifies that the face mesh is to be smoothed.

Coordinate �

Sys.

specifies the reference coordinate system.

Type ————————————————————————

Cartesian � Cylindrical Spherical

specifies the reference coordinate system type.

Global | Local allows you to define the location of the node with respect to

either the Global or Local coordinate system.



Split Quad Meshes

The Split Quad Meshes operation (face quadsplit command) splits quad-

rilateral face mesh elements into triangular elements. To accomplish the split

operation, GAMBIT creates mesh edges between existing nodes of the quad-

rilateral mesh but does not alter the original positions of the mesh nodes in the

process.

As an example of the Split Quad Meshes operation, consider the quad-meshed

face shown in Figure 3-53(a). In this example, the face is bounded by an edge

loop consisting of five edges and has been meshed by means of a Quad:Pave scheme.

(a) Before Split Quad operation (b) After Split Quad operation

Figure 3-53: Split Quad Meshes example

If you perform the Split Quad Meshes operation on the face shown in Figure 3-53(a), GAMBIT splits the quadrilateral mesh elements into triangular ele-

ments to create the mesh shown in Figure 3-53(b).

Excluding Boundary Layer Faces

The Split Quad Meshes form includes an Exclude boundary layer faces option that allows you to prohibit GAMBIT from splitting quad mesh elements in

face boundary layers. As an example of the effect of the Exclude boundary layer faces option, consider the meshed face shown in Figure 3-54. The face is simi-

lar to that shown in Figure 3-53, above, but includes a boundary layer along

the left side.



Boundary layer

Figure 3-54: Quad-meshed face with boundary layer

Figure 3-55 shows the effect of the Exclude boundary layer faces option on the Split Quad Meshes operation for the face shown in Figure 3-54.

(a) Exclude boundary layer faces off (b) Exclude boundary layer faces on

Figure 3-55: Effect of Exclude boundary layer faces option



The effects can be summarized as follows:

• If you do not select the Exclude boundary layer faces option when executing the Split Quad Meshes operation, GAMBIT splits all mesh

quads on the face (see Figure 3-55(a)).

• If you do select the Exclude boundary layer faces option, GAMBIT splits

only the quad mesh elements that do not constitute parts of the bound-

ary layer (see Figure 3-55(b)).

Using the Split Quad Meshes Form

To open the Split Quad Meshes form (see below), click the Split command

button on the Mesh/Face subpad.

The Split Quad Meshes form contains the following specifications.

Faces � specifies the meshed face(s) for which the quad mesh is to be

split into triangular elements.

�� Exclude boundary layer faces

specifies that quad face elements in boundary-layer regions are

to be excluded from the split operation.



3.3.3 Smooth Face Meshes

The Smooth Face Meshes operation (face smooth command) adjusts the

node locations for one or more face meshes. When you smooth a face mesh,

GAMBIT automatically adjusts the mesh node locations to improve the uni-

formity of the spacing between nodes across the face. To smooth a face mesh,

you must specify the following parameters:

• The face(s) for which the mesh is to be smoothed

• The smoothing scheme

Specifying the Smoothing Scheme

GAMBIT provides the following smoothing schemes:

• Length-weighted Laplacian (L-W Laplacian)

• Centroid Area (Centroid Area)

• Winslow (Winslow)

The following table summarizes the basic features of the algorithm employed

by each scheme.

Algorithm Features

Length-weighted Laplacian • Uses the average edge length of the

elements surrounding each node

• Tends to average element edge lengths

Centroid Area • Equalizes areas of adjacent elements

Winslow • Optimizes element shapes with respect

to perpendicularity

• Applies only to quadratic elements



Using the Smooth Face Meshes Form

To open the Smooth Face Meshes form (see below), click the Smooth Mesh command button on the Mesh/Face subpad.

The Smooth Face Meshes form contains the following specifications.

Faces � specifies the face(s) for which the mesh is to be smoothed.

Scheme contains an option button that allows you to specify one of

three smoothing algorithms (see above).

L-W Laplacian � Centroid Area Winslow

specifies the mesh smoothing algorithm.



3.3.4 Set Face Vertex Type

The Set Face Vertex Type operation (face modify command) defines the

characteristics of face meshing and/or boundary layer construction operations

in the vicinity of a specified vertex. The vertex-type specifications also deter-

mine which face meshing scheme GAMBIT selects as the default scheme.

To set the type for one or more vertices, you must specify the following input

parameters.

• Face

• Type

• Vertices

• Boundary layer only option

The Face, Type, and Vertices parameters define the vertex type specification.

The Boundary layer only option specifies whether the specification applies to meshing and/or boundary layer construction operations.

Specifying the Face

GAMBIT vertex types are specific to the faces upon which they are set; there-

fore, to specify the type designation of an individual vertex, you must also

specify a face associated with that vertex. An individual vertex may possess as

many vertex type designations as the number of faces to which it is attached.

For example, it is possible for a vertex to possess a Side type designation with respect to one face and an End type designation with respect to another face.

Specifying Vertex Type

The structure of any face mesh in the vicinity of an individual vertex on its

boundary is a function of the face meshing scheme and vertex type. GAMBIT

provides six vertex types (see Figure 3-56):

• End

• Side

• Corner

• Reversal

• Trielement

• Notrielement



(a) End

End vertex

(c) Corner

Corner

vertex

(d) Reversal

Reversal

vertex

(e) Trielement

Trielement

vertex

(f) Notrielement

Notrielement

vertex

(b) Side

Side vertex

Figure 3-56: Face vertex types

Each vertex type differs from the others in the following ways:

• Number of face mesh lines that intersect the vertex

• Angle between the edges immediately adjacent to the vertex

• Face mesh scheme to which it applies

The following table summarizes the characteristics of the vertex types shown

in Figure 3-56.



Vertex Type

Intersecting

Grid Lines

Angle Between Edges

Applicable

Mesh Scheme

End 0 °<<° 1200 θ Quad:Map Quad:Pave Quad:Submap Quad:Tri Primitive Quad/Tri:Map Quad/Tri:Pave Quad/Tri:Wedge Primitive Tri:Pave

Side 1 °<≤° 216120 θ Quad:Map Quad:Pave Quad:Submap Quad:Tri Primitive Quad/Tri:Map Quad/Tri:Wedge Primitive

Corner 2 °<≤° 5.308216 θ Quad:Map Quad:Submap

Reversal 3 °<≤° 3605.308 θ Quad:Map Quad:Submap

Trielement 0 Acute

(User specified)

Quad:Tri Primitive Quad/Tri:Map Quad/Tri:Wedge Primitive

Notrielement 0 Acute

(User specified) Quad:Tri Primitive Quad/Tri:Map Quad/Tri:Wedge Primitive

� NOTE: GAMBIT ignores vertex types when meshing a face according to the

Pave mesh scheme.

The following sections describe the general effect of each vertex type on the

shape of the face mesh in the vicinity of a specified vertex.



End Vertex Type

When you specify a vertex as the End vertex type and do not specify a Pave meshing scheme, GAMBIT creates the face mesh such that only two mesh

element edges intersect at the vertex (see Figure 3-56(a)). As a result, the

mapped and submapped face mesh patterns on both sides of the End vertex terminate at the edges adjacent to the vertex.

Side Vertex Type

When you specify a vertex as the Side vertex type and do not specify a Pave meshing scheme, GAMBIT creates the face mesh such that three mesh ele-

ment edges intersect at the vertex (see Figure 3-56(b)). GAMBIT treats the

two topological edges that are adjacent to the vertex as a single edge for the

purposes of meshing.

Corner Vertex Type

When you specify a vertex as the Corner vertex type and do not specify a Pave meshing scheme, GAMBIT creates the face mesh such that four mesh element

edges intersect at the vertex (see Figure 3-56(c)). The Corner vertex type can-not be applied to vertices the adjacent edges of which form angles less than

180°.

Reversal Vertex Type

When you specify a vertex as the Reversal vertex type, GAMBIT creates the

face mesh such that five mesh element edges intersect at the vertex (see

Figure 3-56(d)). When you apply a Submap meshing scheme to a face that

includes a Reversal vertex, GAMBIT creates a line of mesh edges that extends

from the Reversal vertex to a topological edge on an opposite side of the face. GAMBIT treats the resulting line and each adjacent edge as a single edge for

the purposes of meshing.

Trielement and Notrielement Vertex Types

When you specify a vertex as the Trielement vertex type, GAMBIT creates a

triangular element (see Figure 3-56(e)) at the vertex, regardless of the default

element type that would otherwise be created using either the Quad/Tri:Map, Tri:Primitive, or Quad/Tri:Wedge Primitive face meshing schemes.

When you specify a Notrielement vertex type, GAMBIT creates a quadrilateral

element at the vertex, regardless of the default element type that would other-

wise be created.



Effect of Vertex Type on Face Meshes

As an example of the general effects of vertex types on face meshes, consider

the planar face shown in Figure 3-57. The following three examples illustrate

the effects of different vertex-type specifications applied to vertices C, F, and

G on the shape of the resulting mesh.

A

C D

G

F E

B

Figure 3-57: Seven-sided planar face



In Figure 3-58, vertices C, F, and G are specified as Side vertices; therefore, GAMBIT treats sides BCD and EFGA as if each were a single edge. As a

result, the entire face represents a mappable region, and GAMBIT creates a

single checkerboard pattern for the mesh.

A: End

C: Side D: End

G: Side

F: Side E: End

B: End

Figure 3-58: Example face mesh—Side inside corner vertex



In Figure 3-59, vertices C, F, and G are specified as Corner, Side, and End type vertices, respectively. As a result, the face is submappable, and GAMBIT

creates two separate checkerboard patterns for the mesh. The upper-left sub-

mapped region is defined by the polygon ABCHFG. The lower-right sub-

mapped region is defined by CDEH. For both regions, the node at point H

serves as an End type vertex for the purposes of mesh creation.

A: End

C: Corner D: End

G: End

F: Side E: End

B: End

H

Figure 3-59: Example face mesh—Corner inside corner vertex



In Figure 3-60, vertices C, F, and G are specified as Reversal, End, and End vertices, respectively. As a result, the face is submappable, similar to that

shown in Figure 3-59. The upper-left submapped region is defined by the

polygon ABCHG. The lower-right submapped region is defined by CDEFH.

Unlike the mesh shown in Figure 3-59, the mesh in Figure 3-60 does not ter-

minate at vertex C. Instead, GAMBIT treats the sides BCH and HCD as single

edges when creating the mesh.

A: End

C: Reversal D: End

G: End

F: End E: End

B: End

H

Figure 3-60: Example face mesh—Reversal inside corner vertex

Meshing Vertex Types vs. Boundary Layer Vertex Types

Vertex type specifications affect two kinds of GAMBIT operations:

• Meshing

• Boundary layer construction

The Set Face Vertex Type form allows you to specify the vertex type for each

operation independently. For example, a given vertex can be specified as End type for meshing operations and Side type for boundary layer construction. The boundary layer characteristic affects the mesh only if a boundary layer is

applied to the face prior to meshing.



As an example of the effect of independent specification of vertex types, con-

sider the square planar face shown in Figure 3-61(a) and (b). For this face,

vertex b is specified as an End vertex for meshing operations and as a Side vertex for boundary layer construction operations.

(a) No boundary layer (b) Boundary layer

a b

cd

a b

cd

Figure 3-61: Effect of independent specification of vertex type

If you mesh the face without first applying a boundary layer, GAMBIT

creates the mesh shown in Figure 3-61(a). However, if you apply a uniform,

five-row boundary layer to edges a-b and b-c before meshing, GAMBIT

creates the mesh shown in Figure 3-61(b). In this case, the boundary layer

dovetails in the corner region because vertex b is specified as a Side vertex for boundary layer construction.

As noted above, the boundary layer vertex type affects the structure of the

mesh only when a boundary layer is applied prior to meshing. As an example

of the effect of boundary layer vertex type on mesh structure, consider the

square planar face shown in Figure 3-62. In Figure 3-62(a), vertex b is speci-

fied as an End vertex for boundary layer operations; in Figure 3-62(b), vertex b is specified as a Side vertex for boundary layer operations. In both cases, vertex b is specified as an End vertex for meshing operations.



(a) Side vertex b (b) End vertex b

a b

cd

a b

cd

Figure 3-62: Effect of boundary layer vertex type

If you apply a uniform, five-row boundary layer to edges a-b and b-c before

meshing the face, GAMBIT creates the meshes shown in Figure 3-62(a) and

(b). In this case, the structure of the mesh in proximity to vertex b varies

according to the specified vertex type. In both cases, if you do not apply a

boundary layer to the edges prior to meshing the face, GAMBIT creates the

mesh shown in Figure 3-61(a), above.

Specifying the Boundary layer only Option

The Boundary layer only option on the Set Face Vertex Type form operates

according to the following rules:

• If you select the Boundary layer only option and change a vertex type, GAMBIT applies the current Set Face Vertex Type specifications only to the boundary layer characteristics of the specified Vertices.

• If you deselect the Boundary layer only option and change a vertex type, GAMBIT applies the current Set Face Vertex Type specifications to both the meshing and boundary layer characteristics of the specified

Vertices.



Using the Set Face Vertex Type Form

To open the Set Face Vertex Type form (see below), click the Set Face Vertex Type command button on the Mesh/Face subpad.

The Set Face Vertex Type form contains the following options and specifica-

tions.

Face � specifies the face upon which the vertex type is to be set.

Type contains a field of six radio buttons that specify the vertex type

for all vertices selected by means of the Vertices list box in the lower part of the form. The available vertex types are End, Side, Corner, Reversal, Trielement, and Notrielement.

Vertices � specifies one or more vertices to which the currently specified

vertex type is applied.

�� Boundary layer only

specifies that any change made to the vertex type specifications

applies only to boundary layers adjacent to the specified

vertices.



3.3.5 Set Face Element Type

The Set Face Element Type operation (default set command for the

MESH.NODES.QUAD default variable) specifies the mesh node configuration

associated with either of two available face element shapes.

To set the face element type, you must specify the node pattern associated

with each of the face element shapes. There are two face element shapes avail-

able in GAMBIT:

• Quadrilateral

• Triangle

Each face element shape is associated with three different node patterns, and

each node pattern is characterized by the number of nodes in the pattern.

Figure 3-63 and Figure 3-64 show the node patterns associated with the quad-

rilateral and triangular face element types, respectively.

(a) 4 node (c) 9 node(b) 8 node

Figure 3-63: Quadrilateral face element types




Figure 3-64: Triangular face element types

When you set a face element type, GAMBIT applies the type to all face ele-

ments of the specified shape. For example, if you specify 8-node quadrilateral

face elements, GAMBIT locates mesh nodes according to the 8-node pattern

for all quadrilateral face elements produced in the subsequent face meshing

operation. (NOTE: For a description of the relationships between edge, face,

and volume element types, see “Set Edge Element Type,” above.)

� NOTE: Finite-element solvers, such as the FIDAP solver, employ higher-

order elements (for example, 8-node and 9-node quadrilateral elements). Finite-

volume solvers, such as FLUENT/UNS, employ only linear elements (for

example, 4-node quadrilateral elements).



Using the Set Face Element Type Form

To open the Set Face Element Type form (see below), click the Set Face Ele-ment Type command button on the Mesh/Face subpad.

The Set Face Element Type form contains the following specifications.

Quadrilateral allows you to specify the quadrilateral face element node

pattern. The available node patterns include 4 node, 8 node, and 9 node.

Triangle allows you to specify the triangular face element node pattern.

The available node patterns include 3 node and 6 node.



3.3.6 Link/Unlink Face Meshes

The Link/Unlink Face Meshes command button allows you to perform the fol-

lowing operations.


Link Face Meshes Creates hard links between faces

Unlink Face Meshes Deletes hard links between faces



� NOTE (1): Face-mesh linking is required for periodic and cyclic boundary

zones, because it insures that meshes match on linked face pairs.

� NOTE (2): When you mesh one of two faces that constitutes part of a linked

pair of faces, GAMBIT stores only one copy of the mesh in the database in

addition to the transformation matrix. As a result, the linking of face meshes

reduces memory use.



Link Face Meshes

The Link Face Meshes operation (face link command) creates a mesh hard

link between two faces. When you create hard links between faces in a set,

GAMBIT associates the faces with each other such that any meshing or split-

ting operation applied to one or more of the faces is similarly applied to all

faces in the set. For example, if you mesh a face that is hard-linked to another

face, GAMBIT meshes both faces according to the grading scheme and

parameters applied to the specified face. Likewise, if you split a boundary

edge of a face that is hard-linked to another face, GAMBIT splits the corres-

ponding edge on the other face.

� NOTE: When you select a face for the Link Face Meshes operation, GAMBIT

automatically highlights the graphic display of any faces to which the face is

currently linked.

To create a mesh hard-link between two faces, you must specify the following

parameters for each face:

• The face to be hard-linked

• A vertex that serves as a reference point for the face mesh

• The orientation of the mesh on the linked face relative to its edge loop

sense

• Whether or not the faces are periodically linked

Specifying Faces

When you hard-link two faces, the faces to be hard-linked must possess

identical numbers of edges. In addition, if a face possesses more than one

edge loop, any face to which it is hard-linked must possess an identical num-

ber of edge loops, and the edge loops that correspond to each other must pos-

sess identical numbers of edges.

As an example of this restriction, consider the six faces shown in Figure 3-65.

Of all possible combinations represented by the faces in the figure, only the

following faces may be hard-linked to each other:

• face.1 and face.2

• face.4 and face.5



(a) (b) (c)

(d) (e) (f)

face.1face.3

face.2

face.4 face.6

face.5

Figure 3-65: Face edge loop hard-link examples

The rules governing the permissibility of hard-links for the faces shown in

Figure 3-65 are as follows.

• face.1 and face.2 can be hard-linked, because each possesses a single edge loop consisting of five edges. Neither can be hard-linked to

face.3, face.4, face.5, or face.6, however, because each of those faces is defined by an outer edge loop consisting of four edges.

• face.3 cannot be hard-linked to face.4, face.5, or face.6, because it pos-sesses a single edge loop, whereas each of the other faces possesses at

least two edge loops.

• face.4 and face.5 can be linked to each other, because each possesses outer and inner edge loops consisting of four and three edges, respec-

tively.

• face.6 cannot be linked to either face.4 or face.5, because it possesses two inner edge loops—one consisting of three edges (triangle) and the

other consisting of one edge (circle).



Specifying Reference Vertices

When you hard-link two faces, you must specify one reference vertex for each

edge loop of each face. The reference vertex determines the relationship

between the edges of each face with respect to meshing. As an example of the

effect of reference vertex specification, consider the two hard-linked faces

shown in Figure 3-66 and Figure 3-67. In both figures, face.1 possesses a boundary layer attached to its left edge.

face.1 face.2

Reference vertices

Figure 3-66: Face hard-link—identical reference vertex positions



face.1 face.2

Reference vertices

Figure 3-67: Face hard-link—differing reference vertex positions

In Figure 3-66, the reference vertices are located at identical positions on each

face, therefore the mesh scheme applied to face.1 is exactly duplicated on face.2. In Figure 3-67, the reference vertex locations differ between faces, therefore the location of the boundary layer on face.2 is different from that on

face.1.

Specifying Mesh Orientation

If you create a hard link between two faces the edge loop senses of which are

reversed relative to each other, you must reverse the orientation of the linked

mesh in order to create identical meshes on both faces. As an example of this

constraint, consider the two hard-linked faces shown in Figure 3-68. The bot-

tom edge of face.1 is graded toward its left endpoint vertex, and the senses of the edge loops for the faces are reversed relative to each other.



face.1 face.2

Reference vertices Edge sense

Figure 3-68: Face hard-link—orientation relative to edge loop sense

If you specify reference vertices at identical positions on both faces, GAMBIT

constructs a mesh on the linked face (for example, face.2) that is different in orientation from that constructed on the specified face (for example, face.1). To create identical meshes on both faces when you specify reference vertices

as shown in Figure 3-68, you must specify the Reverse orientation option when you create the mesh hard link.

Specifying the Periodic Option

The Link Face Meshes command includes a Periodic option that allows you to specify that the faces are periodically linked. Periodically linked faces are

constrained such that they must behave identically to each other with respect

to any virtual edge-split and vertex-move operations. For a general description

of the effect of periodic linking on the boundary edges of periodically linked

faces, see “Link Edge Meshes,” in Section 3.2.3, above.



Using the Link Face Meshes Form

To open the Link Face Meshes form (see below), click the Link command but-

ton on the Mesh/Face subpad.

The Link Face Meshes form contains the following specifications.

Face � specifies the first of two faces to be hard-linked.

Vertices � specifies one or more reference vertices on the first of the hard-

linked faces. (NOTE: You must specify one reference vertex

for each edge loop associated with the face.)

Link With —————————————————————————

Face � specifies the second of two faces to be hard-linked.

Vertices � specifies one or more reference vertices on the second hard-

linked face (see above).

�� Reverse orientation

specifies that the edge meshing on the second of the two hard-

linked faces is reversed relative to the first.

�� Periodic specifies that the faces are to be periodically linked.



Unlink Face Meshes

The Unlink Face Meshes operation (face unlink command) deletes existing

hard links associated with two faces. To delete a hard link, you must specify

both faces associated with the link.

� NOTE: When you select a face for the Unlink Face Meshes operation, GAM-

BIT automatically highlights the graphic display of any faces to which the

face is currently linked.

Using the Unlink Face Meshes Form

To open the Unlink Face Meshes form (see below), click the Unlink command


The Unlink Face Meshes form contains the following specifications.

Faces � specifies the face(s) for which the hard link is to be deleted.

�� Lower topology specifies that any edge hard links that are associated with the

face hard link are deleted along with the face hard link.



3.3.7 Modify Meshed Face / Split Meshed Face

The Modify Meshed Face / Split Meshed Face command button allows you to

perform the following operations.


Modify Meshed Face Converts mesh edges to topological

equivalents

Split Meshed Face Splits a face along lines defined by an

existing mesh

The following sections describe each of these operations.



Modify Meshed Face

The Modify Meshed Face operation (face split command) converts mesh

edges to faceted topological edges and creates faceted faces where appro-

priate. The command can be used to create faceted representations of existing

geometry or to modify geometry associated with imported mesh information.

To perform a Modify Meshed Face operation, you must first create a Mesh edges conversion list—that is, a list of mesh edges that are to be converted to

faceted geometric edges. To create the conversion list, you must specify the

following parameters:

• The meshed face of interest

• The mesh edges that are to be included in the conversion list

Specifying the Meshed Face

You can specify any meshed face for a Modify Meshed Face operation. The shape of the meshed face determines which mesh edges are added to the con-

version list when using the automatic method of mesh-edge specification (see

below).

Specifying the Mesh Edges

GAMBIT provides two methods for adding mesh edges to the Mesh edges conversion list:

• Automatic

• Manual

When you use the automatic method, GAMBIT automatically adds mesh

edges to the conversion list based on the angle between the outward-pointing

normals of any two adjacent mesh element faces. When you use the manual

method, GAMBIT allows you to select specific mesh edges to be added to (or

removed from) the list.

� NOTE (1): To activate the Mesh edges conversion-list picker, you must first

select a meshed face and Shift-right-click in the graphics window to accept the

selection.

� NOTE (2): When you perform a Modify Meshed Face operation, GAMBIT

highlights mesh edges in the graphics window according to the following

default color code:

• Pink—Detected/picked mesh edges

• Light blue—Undetected/unpicked mesh edges



Using the Automatic Method

To employ the automatic method of adding mesh edges to the conversion list,

you must specify an Angle parameter, θmin

. The Angle parameter represents

the minimum angle (in degrees) between outward-pointing normals for any

two faces the common edge of which is to be automatically added to the con-

version list (see Figure 3-69).

Mesh edge to be added to

the conversion list

Angle between normals

θ

Figure 3-69: Automatic-method angle criterion

When you employ the automatic method, GAMBIT applies the Angle ( minθ )

criterion to all mesh element faces associated with the meshed topological

face. If minθθ > for any two mesh element faces, GAMBIT adds their com-

mon mesh edge to the conversion list. If minθθ < , GAMBIT does not add the

mesh edge to the conversion list. If you specify Angle = 0 and employ the

automatic method for the face, GAMBIT adds to the conversion list all of the

mesh edges associated with the face.

As an example of the use of the automatic method, consider the meshed ellip-

tical, cylindrical face shown in Figure 3-70. The face is meshed using a regu-

lar map mesh with 40 intervals on each of the elliptical boundary edges,

resulting in 560 regular quadrilateral mesh elements.



Figure 3-70: Example meshed cylindrical face

If you employ the automatic method of mesh-edge selection and specify an

Angle parameter of 10 (degrees), GAMBIT automatically adds to the conver-

sion list the mesh edges highlighted in Figure 3-71(a). In this case, the

selected edges form straight chains that run the entire length of the cylinder;

therefore, the Modify Meshed Face operation results in the creation of 10 fac-eted faces, each of which is as long as the cylinder itself (see Figure 3-71(b)).

If you specify an Angle parameter of 5 (degrees), GAMBIT automatically

adds to the conversion list the mesh edges highlighted in Figure 3-71(c). In

this case, the list includes longitudinal edges that exist on the less-rounded

regions of the cylinder, and the Modify Meshed Face operation results in the creation of 22 faceted faces (see Figure 3-71(d)).



(a) Selected edges, Angle = 10 (b) Created faces, Angle = 10

(c) Selected edges, Angle = 5 (d) Created faces, Angle = 5

Figure 3-71: Effect of Angle parameter on created faces

� NOTE (1): GAMBIT does not include any lateral mesh edges in this example

(that is, mesh edges that are perpendicular to the cylinder axis), because all

adjacent faces that share common lateral edges are parallel to each other.

� NOTE (2): All faces created by the Modify Meshed Face command are faceted

faces. By default, GAMBIT labels all faceted faces with the prefix “f_”—for

example, f_face.107.

� NOTE (3): When you create faceted faces by means of the Modify Meshed Face command, GAMBIT does not delete the underlying face geometry. For

example, the geometry shown in Figure 3-71(b), above, includes 10 faceted

faces, as well as the original real elliptical face.



Using the Manual Method

When you use the manual method of managing the mesh-edge conversion list,

GAMBIT allows you to perform the following operations, each of which cor-

responds to a separate option on the Modify Meshed Face form.

• Add—Adds mesh edges to the conversion list

• Remove—Removes mesh edges from the conversion list

• Remove spurs—Removes continuous chains of mesh edges from the

conversion list

Adding and Removing Edges

To add or remove a mesh edge to or from the conversion list, you must select

the Add or Remove option, respectively, and specify the mesh edge to be added

or removed. You can specify the mesh edge to be added or removed in the

following ways:

• Input the number corresponding to the mesh edge in the Mesh edges list box.

• Pick the mesh edge in the graphics window.

� NOTE (1): The mesh edge conversion list automatically includes all mesh

edges that exist on the boundary edges of the meshed face. GAMBIT does not

allow you to remove such edges from the conversion list.

� NOTE (2): If you click the Mesh edges pick-list button, GAMBIT displays the

special Mesh Edge List (Multiple) pick-list form. The form differs from ordi-

nary pick-list forms in that it does not include a list of Available mesh edges.

(In most cases, the list of Available mesh edges is too long to be of practical

use.) Otherwise, the form operates according to the principles that govern all

pick-list forms.

Removing Spurs

Spurs are chains of connected mesh edges in the conversion list—such as

those that form the longitudinal edges of the faceted faces shown in Figure

3-71, above. Spurs that do not attach at both ends to other topological edges

constitute dangling spurs (see Figure 3-72).



Dangling spurs

Figure 3-72: Example dangling spurs

When you select the Remove spurs option and specify a mesh edge that con-

stitutes any part of a spur, GAMBIT removes from the conversion list all

edges associated with the spur.

Combining the Automatic and Manual Methods

The Modify Meshed Face command allows you to combine the automatic and

manual methods to create the Mesh edges conversion list. For example, you

can use the automatic method to create the overall conversion list and use the

manual method to modify the list.

Figure 3-73 shows the effect of a combined automatic/manual method on the

meshed elliptical cylinder shown above. In this case, the conversion list is first

created by using the automatic method with an Angle specification of 5 (degrees) then modified using the manual method to add and remove edges

from the list as shown. Figure 3-73(b) shows the faceted faces created from

the resulting Modify Meshed Face operation.



(a) Selected edges

(b) Created faces

Added and removed edges

Figure 3-73: Combined use of automatic and manual methods

� NOTE: To combine the automatic and manual methods, you must use the

automatic method before using the manual method. Each time you input a

value into the Angle input field (or use the Angle slider bar), GAMBIT resets

the conversion list and populates it based only on mesh edges specified using

the current Angle criterion.

Selecting the Entire Meshed Face

You can specify selection of the entire meshed face for conversion in either of

the following ways.

• Use the automatic method with an Angle specification of 0.

• Open the Mesh edges pick-list form, and click All-> to select all meshed

edges in the list.



Using the Modify Meshed Face Form

To open the Modify Meshed Face form (see below), click the Modify Meshed Face command button on the Mesh/Face subpad.

The Modify Meshed Face form contains the following options and specifica-

tions.

Face � specifies the meshed face to which mesh-edge conversion oper-

ation is to be applied.

Mesh edges � specifies the mesh edges in the conversion list.

�� Keep original edge

specifies the retention of any topological edge associated

with a removed mesh edge.

Automatic: —————————————————————————

Angle –��– specifies the minimum angle between normals for adjacent

mesh-element faces for which the common mesh edge is to

be added to the conversion list.

Manual: —————————————————————————

�� Add specifies that the specified mesh edge is added to the con-

version list.



�� Remove specifies that the specified mesh edge is removed from the

conversion list.

�� Remove spurs specifies that all edges included in the spur associated with

the specified mesh edge are removed from the conversion

list.



Split Meshed Face

The Split Meshed Face operation (face split command) splits a meshed

face into two virtual faces.

When you split a face by means of the Split Meshed Face command, GAMBIT

creates two virtual faces that share a common virtual edge. The shape of the

virtual edge is determined by the nodes that define the split path. Once the

virtual faces are created, GAMBIT retains them even if you delete the mesh

that was used to define their shapes.

To split a meshed face by means of the Split Meshed Face command, you must

specify the following parameters.

• The meshed face to be split

• The mesh nodes that define the split path

• The Split edge angle option

Specifying the Face

You can use the Split Meshed Face command to split any real or virtual face

that is currently meshed.

Specifying the Split Path Mesh Nodes

To split a face using mesh nodes, you must specify two or more mesh nodes

that define the path of the split. Two of the mesh nodes must be located on the

edges of the face. The other mesh nodes that define the split path may exist

anywhere else internal to the face, but none of them may lie on one of the

edges of the face.

Figure 3-74 illustrates the effect of splitting a real face by means of the Split Meshed Face form. Figure 3-74(a) shows the mesh and four mesh nodes that

define the split path. Figure 3-74(b) shows the two virtual faces that result

from the split operation.



Split-path mesh nodes

(a) (b)

face.1

v_face.2

v_face.3

Figure 3-74: Face split by mesh nodes

Specifying the Split edge angle Option

The Split edge angle option allows you to specify the characteristics of the chain of edges that separates the faces resulting from the split. When you

select the Split edge angle option and specify a value, GAMBIT creates vertices

only at those mesh nodes the adjacent mesh edges of which are separated by

an angle (in degrees) less than the specified Split edge angle value.

As an example of the effect of the Split edge angle option, consider the meshed

face shown in Figure 3-75(a). The face is square and is meshed using a

triangular pave mesh.



(b) Split edge angle off(a) Original meshed face

(c) Split edge angle = 140º (d) Split edge angle = 90º

Splitting

nodesv_face.2

v_face.3

v_face.2

v_face.3v_face.2

v_face.3

Figure 3-75: Effect of Split edge angle option

If you split the face and do not specify the Split edge angle option, GAMBIT

creates vertices at each mesh node along the split path and joins the vertices

with a chain of straight edges that splits the face (Figure 3-75(b)). If you spec-

ify a Split edge angle value of 140, GAMBIT creates vertices only at those

nodes the adjacent mesh edges of which are separated by an angle less than

140º (Figure 3-75(c)). If you specify a Split edge angle value of 90, GAMBIT

splits the meshed face with a single edge (Figure 3-75(d)).



Using the Split Meshed Face Form

To open the Split Meshed Face form (see below), click the Split Meshed Face command button on the Mesh/Face subpad.

The Split Meshed Face form contains the following specifications.

Face � specifies the face to be split.

Split With —————————————————————————

Nodes � specifies the mesh nodes that define the split path.

�� Split edge angle

specifies that vertices are created only at mesh nodes the adja-

cent mesh edges of which are separated by an angle less than

the Split edge angle value.



3.3.8 Summarize/Check Face Meshes

The Summarize/Check Face Meshes command button lets you perform the

following operations.


Summarize Face Mesh Summarizes general face mesh infor-

mation in the Transcript window

Check Face Meshes Displays face mesh quality informa-

tion in the Transcript window





Summarize Face Mesh

The Summarize Face Mesh operation (face msummarize command) dis-

plays face mesh information in the Transcript window and allows you to highlight specific mesh nodes and/or mesh elements in the graphics window.

The command requires three input parameters:

• Face for which the mesh is to be summarized

• Type of component (elements or nodes) to be summarized

• Specific components to be included in the summary

Specifying the Component Type

To summarize face mesh information in the Transcript window, you must

specify the type of mesh components to be included in the summary. Each

face mesh includes two component types:

• Elements

• Nodes

The type of mesh summary information displayed in the Transcript window depends on the component type (see “Face Mesh Summary Information,”

below).

Selecting Specific Components

GAMBIT provides two methods for selecting specific components (elements

or nodes) to be included in the face mesh summary:

• Picking the components in the graphics window

• Selecting the components by means of a pick list

In most cases, it is preferable to pick the components in the graphics window,

rather than selecting them by means of a pick list, because the component

labels (element or node numbers) are not known prior to component selection.

To pick the components in the graphics window:


2. Click (to activate) the appropriate (Elements or Nodes) pick-list field.

3. Shift-left-click in the graphics window to select each element or node

to be included in the summary.



To select the components by means of a pick list:


2. Click the appropriate (Elements or Nodes) pick-list button to open the Mesh Face List (Multiple) or Mesh Node List (Multiple) form.

3. On the Mesh Face List (Multiple) or Mesh Node List (Multiple) form,

click the All–> pushbutton to populate the list with all elements or

nodes associated with the specified face.

4. In the Mesh Face List (Multiple) or Mesh Node List (Multiple) list, select (highlight) the elements or nodes to be excluded from the summary.

5. Click the <– – – pushbutton to remove the selected (highlighted) ele-

ments or nodes from the list.

� NOTE: The Mesh Face List (Multiple) and Mesh Node List (Multiple) forms do

not include the Available list field that is included on most pick-list forms

because of the number of items that might need to be included in the list field.

A fully meshed model can contain tens of thousands of mesh elements or

nodes, each of which constitutes an Available component. If the Mesh Face List (Multiple) or Mesh Node List (Multiple) form included an Available list field, GAMBIT would need to compile the Available list before opening the form,

thereby delaying the appearance of the form on the GUI.

When you specify any component (element or node) to be included in the

mesh summary, GAMBIT highlights the component in the graphics window.

If you select the Element labels and/or Node labels options, GAMBIT also dis-

plays the element and/or node numbers associated with the specified compo-

nents (see Figure 3-76).



Node numbers Element

numbers

Figure 3-76: Face mesh element and node numbering display

Face Mesh Summary Information

As noted above, the type of mesh summary information displayed in the

Transcript window depends on the type of component being summarized. For

example, element summaries include node connectivity information, which is

not available in node summaries.

Elements Summary Information

If you select the Elements option, the mesh summary includes the following

information for each specified element.

• Element number

• Element type

• Number (count) of nodes associated with the element

• Connectivity of nodes associated with the element

For example, if you select an Elements summary for the face and highlighted

elements shown in Figure 3-76, above, GAMBIT displays the following infor-

mation in the Transcript window.



Summarizing mesh on face.4:

Total nodes: 25

Total elements: 16

Element Type Count Connectivity

----------- --------- -------------- -------------------------

9 quad 4: 12 18 19 13

10 quad 4: 18 21 22 19

14 quad 4: 19 22 8 7

15 quad 4: 22 25 9 8

In this case, the summary indicates that Element 10 is a quad mesh element

connected to nodes 18, 21, 22, and 19.

Nodes Summary Information

If you select the Nodes option, the mesh summary includes the following

information for each specified node.

• Node number

• Coordinates (x, y, z) of the node

• Geometric entity (“owner”) associated with the node

For example, if you select a Nodes summary for the face and nodes 7, 13, and

19 shown in Figure 3-76, above, GAMBIT displays the following information

in the Transcript window.

Summarizing mesh on face.4:

Total nodes: 25

Total elements: 16

Coordinate System: c_sys.1

Node x y z Owner

----------- --------- ---------- --------- -------------

7 5.0000 2.5000 -5.0000 edge.3

13 5.0000 5.0000 -2.5000 edge.8

19 5.0000 2.5000 -2.5000 face.4

In this case, the summary indicates that node 13 is located at the position (5, 5,

-2.5) and is associated with (“owned by”) face.4.



Using the Summarize Face Mesh Form

To open the Summarize Face Mesh form (see below), click the Summarize command button on the Mesh/Face subpad.

The Summarize Face Mesh form contains the following options and specifica-

tions.

Face � specifies the face for which information is to be summarized.

Component —————————————————————————

�� Elements displays summary information for specified elements.

All � Pick


includes all elements or only selected elements.

Pick � specifies the elements for which mesh summary


�� Element labels displays labels (numbers) in the graphics window for all

specified elements.


nodes associated with the specified elements.

�� Nodes displays summary information for specified nodes.

All � Pick


includes all nodes or only selected nodes.



Pick � specifies the nodes for which mesh summary infor-

mation is to be displayed.


specified nodes.



Check Face Meshes

The Check Face Meshes operation (face check quality command) dis-

plays 2-D mesh quality data. When you execute the Check Face Meshes com-

mand, GAMBIT displays the following elements in the Transcript window:

• A table that summarizes 2-D mesh quality statistical information for

all faces specified on the Check Face Meshes form

• A summary statement that includes the total number of inverted mesh

elements and the number of specified faces that contain inverted

elements

Tabular 2-D Mesh Quality Data

The Check Face Meshes tabular output represents the statistical distribution of element quality values for the current default 2-D quality metric. Table 3.1

shows an example of such output for a face mesh evaluated according to the

EquiAngle Skew quality metric. Output such as that shown in Table 3.1 consti-

tutes a numerical representation of the mesh quality histogram that is dis-

played on the Examine Mesh form when you choose the Display Type:Range option (see Section 3.4.2 of the GAMBIT User’s Guide).

Table 3.1: Example Check Face Meshes tabular output

From value To value Count in range % of total count (114)

-------------------------------------------------------------

0 0.1 36 31.58

0.1 0.2 46 40.35

0.2 0.3 20 17.54

0.3 0.4 6 5.26

0.4 0.5 2 1.75

0.5 0.6 4 3.51

0.6 0.7 0 0.00

0.7 0.8 0 0.00

0.8 0.9 0 0.00

0.9 1 0 0.00

-------------------------------------------------------------

0 1 114 100.00

In addition to the tabular output shown in Table 3.1, the Check Face Meshes command displays the minimum and maximum values of element quality for

the set of specified faces, thus:

Measured minimum value: 0.0286973

Measured maximum value: 0.587398



This minimum and maximum element quality information is not available by

means of any other GAMBIT operation.

Specifying the Quality Metric

As noted above, the Check Face Meshes command evaluates 2-D mesh ele-

ment quality according to the current default mesh quality metric. To change

the metric used to evaluate element quality for the Check Face Meshes command, you must modify the default 2-D mesh quality metric by means of

the Edit Defaults form. To do so:

1. Open the Edit Defaults form.

2. Click the MESH tab to open the MESH defaults subform.

3. Select the EXAMINE radio button to display the EXAMINE variables.

4. Modify the ELEMENT_2D_QUALITY variable.

(For a complete description of the procedures required to modify default vari-

ables by means of the Edit Defaults form, see Section 4.2.4 of the GAMBIT

User’s Guide.)

For example, to evaluate 2-D elements on the basis of the Aspect Ratio metric:

1. Use the procedure described above to set Aspect Ratio as the default

quality metric (ELEMENT_2D_QUALITY=2 )

2. Execute the Check Face Meshes command.

� NOTE: Check Face Meshes command tabular output, such as that shown in

Table 3.1, above, includes all 2-D elements that possess shapes for which the

current default quality metric applies. For example, if you specify Aspect Ratio as the default quality metric, the tabular output includes all quadrilateral and

triangular elements associated with the faces specified on the Check Face Meshes form. However, if you specify Diagonal Ratio as the default quality metric, the tabular output includes only quadrilateral elements, because the

Diagonal Ratio metric does not apply to triangular elements.



Summary Statement

The Check Face Meshes summary statement indicates the number of specified

faces that “fail” the mesh check—for example,

0 out of 2 meshed face(s) failed mesh check.

In the context of the Check Face Meshes command, any face that includes at

least one inverted mesh element fails the mesh check.

Using the Check Face Meshes Form

To open the Check Face Meshes form (see below), click the Check command


The Check Face Meshes form contains the following specification.

Faces � specifies the faces for which mesh element quality is to be

evaluated.



3.3.9 Delete Face Meshes

The Delete Face Meshes operation (face delete onlymesh command)

removes the mesh from one or more meshed faces. When you remove a face

mesh, GAMBIT allows you to retain or remove all edge meshes associated

with the face.

Using the Delete Face Meshes Form

To open the Delete Face Meshes form (see below), click the Delete command


The Delete Face Meshes form contains the following options and specifica-

tions.

Faces � specifies the face(s) for which the mesh is deleted.

All � Pick

• All specifies all faces in the model.

• Pick specifies faces selected by means of the Faces list box.

�� Remove unused lower mesh

removes all unused lower-topology meshes associated with the

specified face(s).

MESHING THE MODEL Volume Meshing Commands


3.4 Volume Meshing Commands

The following commands are available on the Mesh/Volume subpad.


Mesh Volumes Creates mesh nodes throughout a

volume

Smooth Volume Meshes Adjusts volume mesh node positions

to improve uniformity of node spacing

Set Volume Element Type Specifies volume element types used


Link Volume Meshes Unlink Volume Meshes

Creates or removes mesh hard links

between volumes

Modify Meshed Volume Converts mesh edges to topological

equivalents

Summarize Volume Mesh Check Volume Meshes

Displays mesh information in the

graphics window; displays 3-D mesh

quality information

Delete Volume Meshes Deletes existing mesh nodes from

volumes

The following sections describe the purpose and operation of each of the

commands listed above.

Volume Meshing Commands MESHING THE MODEL


3.4.1 Mesh Volumes

The Mesh Volumes operation (volume mesh and volume modify com-

mands) creates a mesh for one or more volumes in the model. When you mesh

a volume, GAMBIT creates mesh nodes throughout the volume according to

the currently specified meshing parameters.

� NOTE: When meshing a volume, GAMBIT meshes any unmeshed faces on

the volume boundary before creating the volume mesh. If any newly created

face mesh includes elements the default quality metric of which exceeds the

current default upper limit, GAMBIT aborts the volume meshing operation

without creating the volume mesh.

The default quality metric and default upper limit are specified by means of

two MESH.EXAMINE default variables:

• ELEMENT_2D_QUALITY

• ELEMENT_QUALITY_LIMIT

For example, if you specify

• ELEMENT_2D_QUALITY = 2

• ELEMENT_QUALITY_LIMIT = 0.93

then GAMBIT will abort the volume meshing operation if any 2-D element on

the newly meshed faces possesses an Aspect Ratio quality metric value greater

than 0.93.

GAMBIT does not apply the criteria described above to any boundary faces

that are pre-meshed—that is, meshed prior to the volume meshing operation.

To mesh a volume, you must specify the following parameters:

• Volume(s) to be meshed

• Meshing scheme


• Meshing options



Specifying the Volume

GAMBIT allows you to specify any volume for a meshing operation; how-

ever, the shape and topological characteristics of the volume, as well as the

vertex types associated with its faces, determine the type(s) of mesh scheme(s)

that can be applied to the volume.

Specifying the Meshing Scheme

To specify the meshing scheme, you must specify the following parameters:

• Elements

• Type

• Smoother (Map meshes only)

The Elements parameter defines the shape(s) of the elements that are used to

mesh the volume. The Type parameter defines the meshing algorithm and,

therefore, the overall pattern of mesh elements in the volume. The Smoother specification determines the type of smoothing algorithm (if any) used to

smooth a mapped mesh during the meshing operation.

The following sections describe the parameters listed above and their effects

on the overall volume mesh.

Specifying Scheme Elements

GAMBIT allows you to specify any of the following volume meshing

Elements options. (NOTE: For descriptions of the basic shapes of each of the mesh elements listed below, see Section 3.4.3.)

Option Description

Hex Specifies that the mesh includes only hexahedral elements

Hex/Wedge Specifies that the mesh is composed primarily of hexahedral

elements but includes wedge elements where appropriate

Tet/Hybrid Specifies that the mesh is composed of tetrahedral,

hexahedral, pyramidal, and wedge elements where

appropriate

Each of the Elements options listed above is associated with a specific set of Type options (see below).



Specifying Scheme Type

GAMBIT provides the following volume meshing Type options.

Option Description

Map Creates a regular, structured grid of hexahedral

elements

Submap Divides an unmappable volume into mappable

regions and creates a structured grid of hexahedral

elements in each region

Tet Primitive Divides a four-sided volume into four hexahedral

regions and creates a mapped mesh in each region

Cooper Sweeps the mesh node patterns of specified “source”

faces through the volume

Stairstep Creates a regular hexahedral mesh and a correspond-

ing faceted volume that approximates the shape of

the original volume

TGrid Creates a mesh that consists primarily of tetrahedral

elements but which may also contain hexahedral,

pyramidal, and wedge mesh elements

Hex Core Creates a core of regular hexahedral elements sur-

rounded by transition layers of tetrahedral, pyrami-

dal, and wedge elements. (NOTE: GAMBIT provides

two methods of generating a Hex Core mesh—

GAMBIT native (Native) and TGrid (TGrid).)

As noted above, each of the Elements options is associated with a specific set

of one or more of the Type options. The shaded cells marked with an “××××” in the following table indicate the allowable combinations of Elements and Type options.



Elements Option

Type Option Hex Hex/Wedge Tet/Hybrid

Map ××××

Submap ××××

Tet Primitive ××××

Cooper ×××× ××××

Stairstep ××××

TGrid ××××

Hex Core ××××

� NOTE (1): Of the Type options listed above, only the Cooper option is associ-ated with more than one Elements option. Therefore, in the following sections, the volume meshing scheme types are differentiated from each other only by

their respective Type names—for example, Tet Primitive.

� NOTE (2): When you specify a volume on the Mesh Volumes form, GAMBIT

automatically evaluates the volume with respect to its shape, topological char-

acteristics, and vertex types and sets the Scheme option buttons to reflect a recommended volume meshing scheme. If you specify more than one volume

for a meshing operation, the scheme represented by the Scheme option buttons reflects the recommended scheme for the most recently picked volume. If you

enforce a meshing scheme by means of the Scheme option buttons on the Mesh Volumes form, GAMBIT applies the scheme to all currently picked

volumes.

Each of the Type options listed in the table above is associated with an allow-able set of solvers in the GAMBIT Solver menu on the main menu bar. The

following table shows the correspondence between the meshing Type and the allowable Solver options. (NOTE: The FLUENT 4 solver requires a structured grid, and the NEKTON solver requires hexahedral mesh elements.)



Type Option

Solver Option Map Submap Tet

Primitive Cooper Stairstep TGrid Hex

Core

FIDAP ×××× ×××× ×××× ×××× ×××× ×××× ××××

FLUENT/UNS ×××× ×××× ×××× ×××× ×××× ×××× ××××

FLUENT 5/6 ×××× ×××× ×××× ×××× ×××× ×××× ××××

FLUENT 4 ×××× ×××× ×××× ××××

NEKTON ×××× ×××× ×××× ×××× ××××

RAMPANT ×××× ×××× ×××× ×××× ×××× ×××× ××××

POLYFLOW ×××× ×××× ×××× ×××× ×××× ×××× ××××

Generic ×××× ×××× ×××× ×××× ×××× ×××× ××××

The correspondences shown in this table indicate which meshing schemes can

produce usable meshes for any given solver, but they do not guarantee that all

meshes created using a given meshing scheme will create usable meshes. For

example, the Stairstep and Hex Core meshing schemes can create meshes

usable by the FIDAP solver; however, they are also capable of creating meshes

that cannot be used by FIDAP—for example, those with hanging nodes.



Map Meshing Scheme

When you apply the Map meshing scheme to a volume, GAMBIT meshes the

volume using an array of hexahedral mesh elements, such as those shown in

Figure 3-77.

Figure 3-77: Map meshing scheme—partial array of hexahedral elements

Each mesh element includes at least eight nodes—located at the corners of the

element. If you specify an alternative volume element node pattern, GAMBIT

creates either 20 or 27 nodes per mesh element (see “Set Volume Element

Type,” below).

Specifying the Smoother Algorithm

If you mesh a volume using a Map meshing scheme, you can automatically

smooth the mesh during meshing by means of a Smoother algorithm. (NOTE:

You can manually smooth any existing volume mesh by means of the Smooth Volume Meshes command (see Section 3.4.2, below).)

GAMBIT provides two Smoother options for volumes:

• None—No smoother applied during meshing

• Hilg-Wht— Hilgenstock-White algorithm



If you specify the Hilg-Wht option, you must also specify a Source face. When

meshing the volume, GAMBIT applies the Hilgenstock-White smoothing

algorithm to minimize the effects of node bunching on volume boundary

edges that are connected to (but do not bound) the Source face. Such node bunching can cause element packing within the volume. The Hilg-Wht option is particularly useful whenever one of the boundary faces (the Source face) of the volume is curved.

General Applicability

The Map volume meshing scheme can only be applied to volumes that can be

meshed such that the mesh represents a logical cube. To represent a logical

cube, a volume mesh must satisfy the following general requirements.

1. There must exist exactly eight mesh nodes that are attached to only

three mesh element faces. (These eight mesh nodes comprise the cor-

ners of the logical cube.)

2. Each of the eight corner mesh nodes must be connected to three other

corner mesh nodes by means of a straight chain of mesh edges—that

is, a chain of mesh edges all of which belong to a single logical row of

mesh nodes.

According to the criteria described above, the most basic form of a mappable

volume is a rectangular brick, such as that shown in Figure 3-77, above. For

such a volume, the mesh nodes located at the corner vertices of the brick con-

stitute the corners of the mesh cube.

Although the strict definition of volume mappability is best expressed in terms

of the mesh itself, it is possible to state mappability requirements in terms of

the general geometrical configuration of a given volume. Specifically, volume

mappability criteria may be stated as follows:

To be mappable, a volume should contain six sides, each of which can

be rendered mappable by the correct specification of vertex types.

(For an exception to the criteria described above, see “Mapping Volumes with

Fewer Than Six Faces,” below.)

� NOTE: Any side of the volume may consist of more than one face.

As an example of the application of the general rule stated above, consider the

volumes shown in Figure 3-78.



(a) (b)

(c) (d)

Figure 3-78: Map volume meshing scheme—example volumes

Of the volumes shown in the figure, only the brick shown in Figure 3-78(a) is

mappable in its primitive form. However, it is possible to transform the other

volumes into mappable volumes by means of vertex-type assignments and vir-

tual geometry operations. The following sections describe the operations

required to render each volume mappable.

Transforming Volumes Into Mappable Forms

As noted above, the volumes shown in Figure 3-78(b), (c), and (d) are not

mappable in their primitive forms, but each can be transformed into a mappa-

ble volume by means of either vertex-type specifications or virtual geometry

operations. Specifically, the operations that are required to transform each

volume are as follows.

Figure 3-78 Shape Operation

(b) Pentagonal prism Vertex-type specification

(c) Cylinder Virtual edge-split

(d) Clipped cube Virtual face collapse



Pentagonal Prism—Specifying Vertex Types

To transform the pentagonal prism shown in Figure 3-78(b) into a mappable

volume, you must specify its vertex types such that the top and bottom faces

are mappable. To do so, you must specify one vertex on each of the top and

bottom faces as a Side vertex and all other vertices as End vertices (see Figure 3-79(a)).

(a) (b)

Side

Side

EndEnd

EndEnd

End

End

EndEnd

A

B

C

Figure 3-79: Mappable pentagonal prism volume

Figure 3-79(b) shows the Map volume mesh that results from the vertex speci-

fications shown in Figure 3-79(a). Note that faces A and B in the figure com-

prise one side of the logical mesh cube and that face C, by itself, constitutes

the opposing side.

When you assign vertex types to transform a prism into a mappable volume,

you must specify the vertex types such that the Side vertices on the top and bottom faces are connected to each other by means of a single vertical edge.

For example, if you assign vertex types according to the specifications shown

in Figure 3-80, GAMBIT cannot create a Map volume mesh in the prism,

because the configuration cannot be made to represent a logical mesh cube.



Side

End

End

End

End

End

Side

End

End

End

Figure 3-80: Unmappable pentagonal prism volume



Cylinder—Splitting Edges and Faces

The cylinder shown in Figure 3-78(c) is not mappable in its primitive form,

but it is possible to transform the cylinder into a mappable volume by means

of virtual edge-split and face-split operations. (For descriptions of the virtual

edge-split and face-split operations, see the appendix of this guide.)

If you split the edges that circumscribe the end caps and use the resulting

vertices to split the cylindrical face into four separate faces, the end faces

become mappable (see Figure 3-81(a)), and the cylinder becomes topologi-

cally equivalent to the brick shown in Figure 3-78(a). As a result, the cylinder

can be meshed according to the Map meshing scheme (see Figure 3-81(b)).

(b)(a)

End

End

End

End

End

End

End

End

Figure 3-81: Mappable cylinder



Clipped Cube—Collapsing a Face

The clipped cube shown in Figure 3-78(d) is not mappable in its primitive

form, but it can be rendered mappable by means of a virtual face collapse

operation. (For a description of the virtual face collapse operation, see the

appendix of this guide.) When you collapse the triangular face between its

three neighboring faces, GAMBIT creates the virtual volume shown in Figure

3-82(a).

(b)(a)

Figure 3-82: Mappable brick without corner

The volume shown in Figure 3-82(a) is topologically equivalent to the brick

shown in Figure 3-78(a). If all of its vertices are specified as End vertices, the volume represents a logical meshing cube and can, therefore, be meshed

according to a Map volume meshing scheme (see Figure 3-82(b)).



Mapping Volumes with Fewer Than Six Faces

As a general rule, the Map volume meshing scheme is applicable only to vol-

umes that include six or more faces. It is possible, however, to transform some

volumes that contain fewer than six faces into mappable volumes. As an

example of such a transformation, consider the sliver-shaped volume shown in

Figure 3-83(a). The volume is bounded by four faces and is not mappable in

its primitive form.

(a)

(b)

(c)

a

b

c

d

fe

gh

Figure 3-83: Mappable volume with four faces

You can transform the sliver-shaped volume shown in Figure 3-83 into a map-

pable form by performing a virtual split operation on each of the curved edges

and specifying the vertex types as follows (see Figure 3-83(b)):

• Vertices a, b, c, and d are End vertices with respect to all faces

• Vertices e, f, g, and h are Side vertices with respect to the curved faces and End vertices with respect to the sliver-shaped end caps

Figure 3-83(c) shows the final form of the Map volume mesh.



Submap Meshing Scheme

When you apply the Submap meshing scheme to a volume, GAMBIT subdi-

vides the volume into logical mesh cubes each of which can be mapped

according to a Map meshing scheme.

� NOTE: The Submap volume meshing scheme, cannot be used to mesh vol-

umes that include “dangling” faces—that is, faces that do not constitute parts

of the closed volume boundary.


To be submappable, a volume must be configured such that it satisfies the

following criteria:

• Each face must be either mappable or submappable.

• Opposing submappable faces must be configured consistently with

respect to their vertex types.

The following sections illustrate each of these criteria.

Face Mappability and Submappability

In order for GAMBIT to apply a Submap meshing scheme to a volume, each

face that bounds the volume must be either mappable or submappable. Figure

3-84 shows four volumes, three of which meet the criteria described above.

The volumes shown in Figure 3-84(a), (b), and (c) are submappable, because

the faces of each volume are, themselves, submappable. The volume shown in

Figure 3-84(d) is not submappable, because the end face of the cylindrical

protrusion on the top of the volume is neither mappable nor submappable.



(a) (b)

(c) (d)

Figure 3-84: Submap volume meshing scheme—submappability criterion

Opposing-Face Vertex Types

The face mappability/submappability criterion described above constitutes a

necessary but insufficient condition for volume submappability. It is possible,

for example, to construct a volume that cannot be meshed according to the

Submap meshing scheme even though all of its faces are either mappable or

submappable.

To apply the Submap meshing scheme to a volume, the face vertex types must

be specified such that the face submap meshes on opposing faces of the

volume are similar in shape and form. As an example of this requirement,

consider the volume shown in Figure 3-85. The volume consists of an L-

shaped brick the outside corner of which is truncated at an angle.



(a)

(c)

End

Corner

Side

End

Corner

Side

End

Reversal

End

End

Reversal

End

End

Corner

Side

End

Reversal

End

(b)

Figure 3-85: Submap volume meshing scheme— L-shaped volume

The L-shaped faces that comprise the top and bottom sides of the volume can

be submapped in a number of ways, each of which is a function of the vertex

types that are assigned to the faces. Figure 3-85 shows face submap meshes

that result from three different configurations of vertex types.

The configurations shown in Figure 3-85(a) and (b) can be meshed according

to the Submap volume meshing scheme, because the vertex types and meshes

on the top and bottom faces of the volume are consistent with each other. By

contrast, GAMBIT cannot apply the Submap volume meshing scheme to the

volume shown in Figure 3-85(c), because the Submap meshes on the top and

bottom faces differ in form.



Tet Primitive Meshing Scheme

The Tet Primitive volume meshing scheme applies only to volumes that consti-

tute logical tetrahedra. To constitute a logical tetrahedron, a volume must

include only four sides, each of which constitutes a logical triangle. When you

apply the Tet Primitive meshing scheme, GAMBIT creates Tri Primitive meshes

on each of the faces of the tetrahedron, then subdivides the volume into four

hexahedral quadrants and creates a Map-type volume mesh in each quadrant.

As an example of the Tet Primitive meshing scheme, consider the tetrahedral

volume shown in Figure 3-86(a). If you apply the Tet Primitive meshing scheme

to the volume, GAMBIT creates Tri Primitive meshes on each face (see Figure

3-86(b)), then subdivides the volume into four quadrants and meshes each

quadrant with hexahedral mesh elements. Figure 3-86(c) shows a cutaway

view of the final mesh.

(a)

(c)

(b)

Figure 3-86: Tet Primitive volume meshing scheme



Cooper Meshing Scheme

When you apply the Cooper meshing scheme to a volume, GAMBIT treats the

volume as consisting of one or more logical cylinders each of which is com-

posed of two end caps and a barrel (see Figure 3-87). Faces that comprise the

caps of such cylinders are called “source” faces; faces that comprise the bar-

rels of the cylinders are called “non-source” faces. (For restrictions related to

the specification of faces for the Cooper meshing scheme, see “Face

Characteristics,” below.)

Non-source

faces

Source face

Source face

(a) Original volume (b) Logical cylinder

Cap

Barrel

Cap

Figure 3-87: Cooper volume meshing scheme—logical cylinder

The Cooper meshing scheme involves the following operation sequence.

1. Create Map and/or Submap meshes on each of the non-source faces.

2. Imprint the source faces onto each other.

3. Mesh the source faces.

4. Project the source-face mesh node patterns through the volume.

As an example of the procedure outlined above, consider the volume shown in

Figure 3-88. The volume represents the union of a cube, a cylinder, and a tri-

angular prism.



Figure 3-88: Cooper volume meshing scheme—example volume

If you apply the Cooper meshing scheme to the volume shown in Figure 3-88,

GAMBIT performs the following operations (see Figure 3-89).

1. Mesh the non-source faces (see Figure 3-89(a)).

2. Imprint the source faces onto each other (see Figure 3-89(b)). (NOTE:

Regions A’ and B’ represent the imprinting of faces A and B, respec-

tively.)

3. Mesh each of the source faces (see Figure 3-89(c)).

4. Project the source-face mesh node patterns through the volume (see

Figure 3-89(d)).



B’

BA’

A

(a) (b)

(c) (d)

Figure 3-89: Cooper volume meshing scheme—example volume


In general, the Cooper meshing scheme applies to volumes that demonstrate

either of the following characteristics.

• At least one face is neither mappable nor submappable.

• All faces are mappable or submappable, but the vertex types are speci-

fied such that the volume cannot be divided into mappable subvolumes

(see “Submap Meshing Scheme: Opposing-Face Vertex Types,”

above).

Faces that meet either of the criteria outlined above, as well as those that are

logically parallel to such faces, constitute source faces for the volume and the

end caps of the corresponding logical cylinder.

� NOTE: The Submap volume meshing scheme, described above, constitutes a

special version of the Cooper meshing scheme. If a volume is configured such

that it can be meshed by either the Submap scheme or the Cooper scheme, it is

usually desirable to mesh the volume by means of the Submap scheme.



Face Characteristics

The Cooper volume meshing scheme imposes the following restrictions on the

volumes to which it applies.

• All non-source faces must be mappable or submappable.

• Source faces onto which a mesh will be imprinted must not be previ-

ously meshed.

• Both caps of the logical cylinder can include interior edge loops, but

the loops must not partially intersect (see below).

• Source faces that are linked to other faces must be linked such that

they do not interfere with the Cooper meshing algorithm. (For a

description of face mesh links, see “Link Face Meshes” in Section

3.3.6.)

Figure 3-90 shows four volumes that illustrate the application of these criteria.

(a) (b)

A

C

B

A

B

(c) (d)

A

B

Figure 3-90: Non-Cooper-able volumes

The volumes shown in Figure 3-90 violate the restrictions outlined above for

the following reasons.



Volume Criterion Reason

Figure 3-90(a) (1) It is impossible to construct a logical cyl-

inder the barrel of which is mappable.

Figure 3-90(b) (2) GAMBIT cannot imprint the mesh from

faces B and C onto face A, because face A

possesses an existing mesh.

Figure 3-90(c) (3) Opposing faces (A and B) that constitute

the caps of the logical cylinder contain

interior edge loops the projections of

which overlap.

Figure 3-90(d) (4) Face A is linked to face B, therefore

GAMBIT cannot imprint the face A mesh

onto face B, because the imprint would

violate the operation of the mesh link.

As noted above, cap faces on the logical cylinder of the Cooper-able volume

can include interior edge loops, but the projections of the loops must not par-

tially intersect each other, as they do in Figure 3-90(c). Figure 3-91 shows two

allowable cases involving interior edge loops on the caps of the logical

cylinder. Figure 3-91(a) is Cooper-able because the projections of the interior edge loops do not intersect each other at all. Figure 3-91(b) is Cooper-able because the interior edge loops fully intersect. (NOTE: If such fully intersect-

ing edge loops are premeshed, the mesh specifications on both loops must be

identical to each other.)



(a) (b)

Figure 3-91: Cooper-able volumes with internal edge loops

Specifying Source Faces

When you apply the Cooper volume meshing scheme to a volume, you must

specify the source faces that define the end caps of the logical cylinder. The

source faces also define the longitudinal direction of the logical cylinder. For

certain volumes, there exist more than one valid set of source faces. For such

volumes, the final form of the mesh depends, in part, on the selection of

source faces.

� NOTE: When you specify a Cooper meshing scheme for a volume, GAMBIT

automatically determines which faces are likely source faces. To override the

automatically selected set of source faces, specify an alternative set of faces

on the Mesh Volumes form.

As an example of the effect of source-face selection on a mesh, consider the

annular volume shown in Figure 3-92. The volume includes four faces—the

end faces, labeled A and B, and the inner and outer cylindrical faces, labeled

C, and D, respectively.



A

B

C

D

Figure 3-92: Annular volume

If you mesh the annular volume by means of a Cooper volume meshing

scheme and specify faces A and B as the source faces, GAMBIT maps the

inner and outer cylinders and paves the end faces, then sweeps the paved mesh

through the annular volume along its axis. The resulting mesh appears as

shown in Figure 3-93(a), below.



(a) (b)

Figure 3-93: Cooper mesh of an annular volume, end source faces

If you specify faces C and D as the source faces, GAMBIT maps the end faces

and paves the inner and outer cylindrical faces, then sweeps the paved mesh

node pattern in a radial direction through the volume. The resulting mesh

appears as shown in Figure 3-93(b).

� NOTE (1): In the example given above, the inner and outer faces are regular

in shape, therefore, the paved meshes on the cylindrical faces are identical in

appearance to mapped mesh node patterns.

� NOTE (2): There are no restrictions on the types of face-meshing schemes

that can be applied to faces that constitute source faces for the Cooper volume

meshing scheme. For example, if you apply a Tri:Pave meshing scheme to a

source face and employ a Cooper meshing scheme, GAMBIT creates wedge

elements in the meshed volume.



Stairstep Meshing Scheme

The Stairstep meshing scheme creates and meshes a faceted volume the shape

of which approximates the volume to be meshed. GAMBIT does not mesh the

original volume itself, and the created faceted volume is not connected to any

existing geometry—including geometry to which the original volume is con-

nected.

As an example of the effect of the Stairstep meshing scheme, consider the vol-

ume shown in Figure 3-94. The volume is an elliptical cylinder 10 units long

with major and minor axis radii of 5 and 3 units, respectively.

Figure 3-94: Stairstep meshing scheme—original elliptical, cylindrical volume

If you mesh the elliptical cylinder shown in Figure 3-94, above, by means of

the Stairstep scheme using an overall interval size of 0.75, GAMBIT creates

and meshes the faceted volume shown in Figure 3-95. Note that the shape of

the faceted volume crudely approximates the shape of the original elliptical

cylinder and that all mesh elements are cubic hexahedra of uniform size.



Figure 3-95: Stairstep meshing scheme—creation of faceted volume

Stairstep Mesh Refinement

If you apply the Stairstep meshing scheme to a volume for which a size func-

tion has been attached, GAMBIT refines the mesh in the region of the size

function. For example, if you attach a size function to the elliptical front face

of the volume shown in Figure 3-94, above, and specify a start size, growth

rate, and size limit of 0.2, 1.3, and 0.75, respectively, the Stairstep scheme

produces the meshed, faceted volume shown in Figure 3-96. In this case, the

mesh elements are small near the elliptical face and large in the bulk volume.

� NOTE (1): GAMBIT ignores mesh interval size specifications when meshing

a volume to which a size function is attached.

� NOTE (2): Refined Stairstep meshes often include hanging nodes—that is,

mesh nodes that bisect other mesh element edges (see Figure 3-96).



Hanging node

Figure 3-96: Stairstep meshing scheme—faceted volume with transition region

GAMBIT provides two options for refining the mesh in the Stairstep scheme.

One option allows the existence of hanging nodes such as those shown in

Figure 3-96. The other option disallows the existence of hanging nodes by

propagating the refined mesh throughout the entire volume. You can select the

Stairstep mesh refinement option by means of a GAMBIT default variable

named STAIRSTEP_MESH_TYPE. To modify the variable:


2. Access the MESH default definition subform.

3. Choose the CARTESIAN option.

4. Select and modify the STAIRSTEP_MESH_TYPE default variable.

The value of the STAIRSTEP_MESH_TYPE default variable affects Stairstep mesh refinement in the following manner.

Value Description

0 Allows hanging nodes in the region of mesh refinement

1 Disallows hanging nodes by propagating the refined mesh

throughout the volume



As an example of the effect of the STAIRSTEP_MESH_TYPE default variable

on the Stairstep mesh, consider the volume shown in Figure 3-97. The volume

consists of a cube with a spherical cutout in one corner. Each edge of the

cube is 10 units long, and the sphere radius is 3 units.

Figure 3-97: Stairstep meshing scheme—cube with cutout corner

Figure 3-98 shows the effect of the STAIRSTEP_MESH_TYPE default variable

value on the final Stairstep mesh configuration. In Figure 3-98(b) and Figure

3-98(c), a size function with a start size, growth rate, and size limit of 0.25,

1.5, and 1.0, respectively, has been attached to the curved, cut-out face.



(a) STAIRSTEP_MESH_TYPE = 0 (b) STAIRSTEP_MESH_TYPE = 1

Figure 3-98: Effect of STAIRSTEP_MESH_TYPE default variable


The Stairstep meshing scheme is applicable to all volumes.



TGrid Meshing Scheme

When you mesh a volume by means of the TGrid meshing scheme, GAMBIT

attempts to create a mesh that consists primarily of tetrahedral mesh elements

but which can also contain hexahedral, pyramidal, and wedge elements where

appropriate. Hexahedral, pyramidal, and wedge elements are typically created

in regions that are adjacent to pre-meshed faces and/or affected by pre-exist-

ing boundary layers (see “Effect of Pre-meshed Faces” and “Effect of

Boundary Layers,” below).

As an example of the TGrid meshing scheme, consider the cubic volume

shown in Figure 3-99(a). The faces of the cube are unmeshed and the volume

does not serve as an attachment entity for any boundary layer. If you mesh the

volume by means of the TGrid scheme, GAMBIT creates a mesh composed

solely of tetrahedral elements such as those shown in Figure 3-99(b). (NOTE:

The elements shown in Figure 3-99(b) represent only a few of those created in

the meshing operation.)

(a) Unmeshed cube (b) Simple TGrid mesh

Figure 3-99: Simple TGrid meshing scheme



Effect of Pre-meshed Faces

If any of the volume boundary faces are pre-meshed using quadrilateral mesh

elements prior to volume meshing, the TGrid scheme (by default) creates a

layer of pyramidal mesh elements adjacent to the pre-meshed face. For

example, if you pre-mesh the bottom face of a cube using quadrilateral ele-

ments, as shown in Figure 3-100(a), the TGrid scheme creates a layer of

pyramidal elements adjacent to the pre-meshed face (see Figure 3-100(b)).

The TGrid scheme produces tetrahedral elements throughout the rest of the

cube.

(a) Quad face mesh (b) Pyramidal mesh elements

Figure 3-100: Effect of pre-meshed face on TGrid scheme

� NOTE (1): You can alter the default TGrid meshing behavior illustrated in

Figure 3-100, above, by means of the MESH.TETMESH.QUAD_SURFACE_

SPLIT default variable (see “Effect of QUAD_SURFACE_SPLIT Default

Variable,” below).

� NOTE (2): In general, it is advisable to avoid creating quadrilateral face mesh

elements with aspect ratios greater than five (5) on the boundaries of any vol-

ume to be meshed by means of the TGrid meshing scheme. Face mesh ele-

ments with high aspect ratios produce highly skewed transition pyramidal

elements, and the subsequent TGrid scheme may fail or produce low-quality

elements.



Effect of Boundary Layers

If one or more boundary layers are attached to a volume prior to meshing, the

TGrid scheme generates hexahedral or wedge elements in the regions affected

by the boundary layer(s). The types of elements generated depend, in part, on

whether or not the boundary layer source faces are pre-meshed with quadrilat-

eral elements prior to creation of the volume mesh.

Boundary Layers Without Pre-meshed Source Faces

If a boundary layer source face is not pre-meshed with quadrilateral elements

prior to meshing the volume, the TGrid scheme automatically meshes the

source face with triangular elements and creates wedge elements in the bound-

ary layer region. As an example of this behavior, consider the cube shown in

Figure 3-101(a). In this case, a boundary layer has been applied to the bottom

face of the cube, and the bottom (source) face is not pre-meshed. If you apply

the TGrid meshing scheme to the cube, GAMBIT generates wedge elements in

the boundary layer region such as those shown in Figure 3-101(b). (NOTE:

The wedge elements shown in Figure 3-101(b) represent only a portion of all

elements created in the boundary layer region.)

(a) Boundary layer (b) Wedge mesh elements

Figure 3-101: Effect of boundary layer with non-pre-meshed source face

In the region of the cube that lies outside the boundary layer, the TGrid scheme

generates tetrahedral elements such as those shown in Figure 3-99(b), above.



Boundary Layers with Pre-meshed Source Faces

If a boundary layer source face is pre-meshed with quadrilateral elements

prior to meshing the volume, the TGrid scheme retains the quadrilateral face

elements and creates hexahedral elements in the boundary layer region. As an

example of this behavior, consider the cube shown in Figure 3-102(a). In this

case, a boundary layer has been applied to the bottom face of the cube, and the

bottom (source) face is pre-meshed with quadrilateral elements. If you apply

the TGrid meshing scheme to the cube, GAMBIT generates hexahedral ele-

ments in the boundary layer region (see Figure 3-102(b)).

(a) Boundary layer with

pre-meshed face

(b) Hexahedral mesh elements

Figure 3-102: Effect of boundary layer with pre-meshed source face

In addition to creating hexahedral elements in the boundary layer region for

this case, the TGrid scheme generates a layer of pyramidal elements on the

boundary layer cap (see Figure 3-103(a)) and fills the rest of the volume with

tetrahedral elements, some of which are shown in Figure 3-103(b).



(a) Pyramidal elements (b) Tetrahedral elements

Figure 3-103: Pyramidal and tetrahedral elements with pre-meshed source

face

Effect of QUAD_SURFACE_SPLIT Default Variable

GAMBIT allows you to modify the default TGrid meshing behavior described

above for volumes with boundary faces that are pre-meshed with quadrilateral

elements. The modification is made by means of the MESH.TETMESH.QUAD_

SURFACE_SPLIT default variable, which specifies whether GAMBIT splits

quadrilateral elements on pre-meshed faces and/or boundary layer caps prior

to applying the TGrid meshing scheme. Allowable values for the QUAD_

SURFACE_SPLIT default variable are as follows.

Value Split Elements on Faces Split Elements on Caps

0 (Default) No No

1 Yes No

2 No Yes

3 Yes Yes



As an example of the effect of the QUAD_SURFACE_SPLIT default variable on

volume meshes generated by the TGrid scheme, consider the cubic volume

shown in Figure 3-104. The top and bottom faces of the cube are pre-meshed

with quadrilateral elements, and the bottom face serves as the source face for a

boundary layer.

Figure 3-104: Cube with boundary layer and pre-meshed faces

Figure 3-105 and Figure 3-106 illustrate the effect of the QUAD_SURFACE_

SPLIT value on mesh-element splitting for the top face and boundary layer

cap. (NOTE: The quadrilateral elements on the pre-meshed bottom face are

not split regardless of the QUAD_SURFACE_SPLIT value because the bottom

face serves as a source face for the boundary layer.)



(a) QUAD_SURFACE_SPLIT = 0 (b) QUAD_SURFACE_SPLIT = 1

Figure 3-105: Effect of QUAD_SURFACE_SPLIT values 0 and 1

(a) QUAD_SURFACE_SPLIT = 2 (b) QUAD_SURFACE_SPLIT = 3

Figure 3-106: Effect of QUAD_SURFACE_SPLIT values 2 and 3



Applying Meshed Size Functions on Boundary Layer Caps

When you apply the TGrid meshing scheme to a volume to which boundary

layers are attached, you can automatically apply a meshed size function at the

boundary layer cap. This capability is invoked by the Meshed S.F. on B.L. cap option on the Mesh Volumes form.

� NOTE (1): If you select the Meshed S.F. on B.L. cap option when meshing a

volume to which boundary layers are not attached, GAMBIT ignores the

option when applying the TGrid meshing scheme.

� NOTE (2): The Meshed S.F. on B.L. cap option is not affected by the Ignore size functions option on the bottom of the Mesh Volumes form.

To apply a meshed size function to a boundary layer cap, you must specify

two parameters: Growth rate and Max. size. For a description of meshed size

functions and the effect of these parameters, see “Create Size Function” in

Section 5.2.2 of this guide.

As an example of the effect of the Meshed S.F. on B.L. cap option, consider the cubic volume shown in Figure 3-107. Two of the bottom edges (a and b) are

graded to create increasing mesh density near the front corner of the cube; the

other two (c and d) are meshed uniformly.

a

d c

b

Figure 3-107: Cube with boundary layer and pre-meshed edges



Figure 3-108 illustrates the effect of the S.F. on B.L. cap option on the TGrid volume mesh. For this example, the effect can be summarized as follows.

• If you do not select the S.F. on B.L. cap option, the TGrid scheme gener-

ates a mesh that includes highly skewed elements above the boundary

layer cap near the front corner of the cube (see Figure 3-108(a)).

• If you select the S.F. on B.L. cap option, the TGrid scheme generates a

mesh such as that shown in Figure 3-108(b), the elements of which are

well-formed in the front corner region above the boundary layer cap.

(a) No size function (b) Size function

Figure 3-108: Effect of S.F. on B.L. cap option



Hex Core Meshing Schemes (Native and TGrid)

GAMBIT provides two types of Hex Core meshing schemes—Hex Core (Native) and Hex Core (TGrid). Both schemes employ the same general technique for

generating the mesh but differ from each other with regard to the characteris-

tics of the central mesh core (see “Hex Core Scheme Types,” below). In

general, when you apply either scheme to a volume, GAMBIT performs the

following sequence of operations:

1. Generate a regular hexahedral mesh throughout the imaginary rectan-

gular “bounding box” that surrounds the volume.

2. Create the “hex core” by removing all elements that either exist out-

side the volume or intersect the volume boundaries. (NOTE: By

default, GAMBIT also removes the inner layer of elements immediate-

ly adjacent to those that intersect the volume boundaries.)

3. Mesh the region between the hex core and the volume boundaries

using pyramidal, tetrahedral, and wedge elements, as appropriate.

As a general example of this type of meshing scheme, consider the elliptical

cylinder shown in Figure 3-94, above. If you mesh the volume by means of a

Hex Core (Native) meshing scheme with an element size of 0.5, GAMBIT

produces a mesh the cross section of which is shown in Figure 3-109.

Figure 3-109: General Hex Core meshing scheme—cross section



The mesh shown in Figure 3-109 consists of a core of hexahedral elements

surrounded by a transition region of pyramidal elements adjacent to the core

itself and a shell of tetrahedral elements filling the remainder of the volume.

The existence of the hex core significantly reduces the total number of mesh

elements relative to that of a purely tetrahedral mesh.

Effect of Internal Dangling Faces

If the volume to be meshed includes an internal dangling face, GAMBIT

treats the face as a boundary face with respect to construction of the hex core.

That is, GAMBIT constructs the mesh such that layers of pyramidal and

tetrahedral elements can exist between the core and the dangling face. Figure

3-110 illustrates the effect of an internal dangling face for the mesh core of the

elliptical cylinder shown in Figure 3-109, above.

Dangling face

(a) Original core (b) Core with dangling face

Figure 3-110: General Hex Core meshing scheme—with internal dangling face



Hex Core Scheme Types

As noted above, GAMBIT provides two types of Hex Core meshing schemes:

• Hex Core (Native)—GAMBIT native scheme

• Hex Core (TGrid)—TGrid scheme

Each scheme type includes its own set of options that allow you to control

mesh characteristics. The specific effects of each method vary according to

the geometry of the volume(s) being meshed.

Hex Core (Native) Scheme

The Hex Core (Native) meshing scheme produces a core of uniformly sized

hexahedral elements surrounded by pyramidal and/or tetrahedral elements.

Specification of the Hex Core (Native) scheme involves the following para-

meters:

• Offset layers value

• Quad surface split option

• Allow hanging nodes option

The Offset layers value allows you to control the size of the hex core. The Quad surface split and Allow hanging nodes options affect characteristics of both the hex core and the surrounding mesh.

Offset layers Value

As noted above, GAMBIT creates the core of a hex-core mesh by generating a

hexahedral mesh throughout the volume “bounding box” and removing the

elements that either exist outside or intersect the volume boundaries. In

addition, GAMBIT removes at least one inner layer of elements immediately

adjacent to those that intersect the volume boundaries. When using the Hex Core (Native) scheme, you can specify the removal of additional element layers

by means of the Offset layers value.

As an example of the effect of the Offset layers specification, consider the two hex cores shown in Figure 3-111. Both hex cores are generated by meshing a

conical cylinder using the Hex Core (Native) scheme. They differ from each

other only with regard to their Offset layers values.



(a) Offset layers = 2 (b) Offset layers = 3

Figure 3-111: Effect of Offset layers value on conical cylinder hex cores

The hex core shown in Figure 3-111(a) is larger than that of Figure 3-111(b)

because fewer of its outer layers have been removed in the mesh generation

process.

� NOTE: The Offset layers value must be greater than or equal to two (2), so

that the mesh can include both tetrahedral elements adjacent to the volume

boundaries and pyramidal elements in the surrounding region.

Quad surface split Option

The Quad surface split option allows you to control the types of face elements

created on the hex-core boundary. If you select the option, GAMBIT splits

(diagonally) all quadrilateral face elements on the hex-core boundary, thereby

replacing them with triangular elements. As a result, the mesh created adja-

cent to the hex-core boundary contains tetrahedral elements rather than the

pyramidal elements that would be created if the quadrilateral face elements

were not split. (NOTE: If you do not select the Quad surface split option, GAMBIT may still split some hex-core boundary elements when generating

the mesh.)



In addition to splitting the hex-core boundary face elements, the Quad surface split option automatically smoothes the mesh on the hex core boundary,

thereby slightly warping the outer hex-core elements. Figure 3-112 shows the

effect of the option on the outer shape of the hex core for the mesh shown in

Figure 3-111(b), above. (NOTE: The inner hex-core elements are not affected

by the automatic smoothing operation (see Figure 3-113).)

(a) Quad surface split = Off (b) Quad surface split = On

Figure 3-112: Effect of Quad surface split option on outer hex-core elements



Smoothed

outer layer

Unsmoothed

inner core

Figure 3-113: Effect of Quad surface split option on hex core regions

� NOTE (1): The splitting of the quadrilateral face elements results in the

creation of a “nonconformal” mesh hex-core boundary interface. If the Hex Core (Native) mesh does not include hanging nodes (see below), the non-

conformal interface consists of two triangular elements for each quad element

at the boundary surface. If the mesh does include hanging nodes, the non-

conformal interface can consist of two, three, or four triangular elements for

each quadrilateral element. (NOTE: Hanging nodes produce nonconformal

meshes even if you do not split the quadrilateral elements at the hex-core

boundary.)

In either case, when you export a nonconformal mesh produced by a Hex Core meshing scheme, GAMBIT includes information in the exported mesh file

that allows the solver to process the nonconformal mesh data without further

input from the user.



� NOTE (2): It is possible to produce a nonconformal mesh by meshing adja-

cent, unconnected volumes by means of different schemes. For example, if

you create a volume consisting of two rectangular bricks that are adjacent but

unconnected by a common face, then mesh one brick with a Map scheme and

the other with a TGrid scheme, the resulting mesh includes a nonconformal

interface at the boundary between the two volumes. In such cases, GAMBIT

does not include information concerning the nonconformity in the exported

mesh file. If the two volumes represent a continuous region in the model (for

example, a flow channel), the user must explicitly specify the nonconformity

when importing the mesh into the solver.

Allow hanging nodes Option

If you select the Allow hanging nodes option, GAMBIT permits the creation of

hanging nodes when generating the Hex Core (Native) mesh. Otherwise,

GAMBIT prohibits the creation of hanging nodes.

Hex Core (TGrid) Scheme

The Hex Core (TGrid) meshing scheme differs from the Hex Core (Native) scheme in that its hex core can consist of hexahedral elements of various

sizes. Specifically, a Hex Core (TGrid) hex core typically consists of an inner core of larger elements surrounded by one or more buffer layers of smaller

elements. The element size in each succeeding buffer layer decreases toward

the hex core boundary (see “Buffer layers Value,” below).

Specification of the Hex Core (TGrid) scheme involves the following para-

meters:

• Peel layers value

• Buffer layers value

• Size limit option

The Peel layers value allows you to control the general size of the hex core. The Buffer layers value determines the general number of buffer. The Size limit value determines the maximum element size in the hex core.

Peel layers Value

The effect of the Peel layers value for the Hex Core (TGrid) meshing scheme is

similar to that of the Offset layers value for the Hex Core (Native) scheme (see

“Offset layers Value,” above.) Specifically, the Peel layers value determines

the number of outer layers of hexahedral elements that are removed when

creating the hex core.



Buffer layers Value

As noted above, a Hex Core (TGrid) hex core typically consists of an inner core of larger elements surrounded by one or more buffer layers of smaller

elements. The Buffer layers value allows you to specify (generally) the number

of buffer layers and to thereby influence the shape and characteristics of the

hex core.

As an example of the effect of the Buffer layers value on a Hex Core (TGrid) mesh, consider the volume shown in Figure 3-114, the geometry of which

represents a catalytic converter. The mesh cross sections shown in Figure

3-115 illustrate the general effect of the Buffer layers value on the character-istics of the hex core for this example.

Figure 3-114: Catalytic converter volume



(a) Buffer layers = 0 (b) Buffer layers = 2

Figure 3-115: Hex Core cross section—effect of Buffer layers value

Size limit Value

The Size limit value determines the maximum element size in the hex core.

GAMBIT provides two Size limit options:

• Auto—Uses the Spacing:Interval size value as the hex core size limit

• Manual—Allows you to specify the Size limit value

If you select the Manual option and specify a Size limit of 0, GAMBIT uses an

internal default TGrid hexcore size-limit value; otherwise, GAMBIT uses the

user-specified Size limit value.

Figure 3-116 illustrates the general effect of the Size limit value on the hex core characteristics for the catalytic-converter geometry shown in Figure

3-114, above.



(a) Size limit = 5 (b) Size limit = 10

Figure 3-116: Hex Core cross section—effect of Size limit value

Specifying the Element Size

The procedures outlined above require that the specified element size is small

enough to allow both the creation of a hexahedral core and two layers of ele-

ments (pyramidal and tetrahedral) surrounding the core. If you specify an

element size that is too large to accommodate both the core and the transition

layers, GAMBIT meshes the volume using only tetrahedral elements. For

example, if you employ the Hex Core (Native) meshing scheme for the elliptical

cylinder shown in Figure 3-94, above, and specify an element size of 1,

GAMBIT creates a mesh the cross section of which is shown in Figure 3-117.



Figure 3-117: Hex Core (Native) meshing scheme—element size = 1


The Hex Core (Native) and Hex Core (TGrid) meshing schemes are applicable to

all volumes but is useful mainly for volumes with large internal regions and

few internal boundaries such as intrusions or holes.

Specifying Volume Meshing Options

GAMBIT includes the following universal options on the Mesh Volumes form:

• Mesh

• Remove old mesh

• Remove lower mesh


Mesh Option

If you select the Mesh option, GAMBIT meshes the picked volume(s) accord-

ing to the parameters as currently specified on the Mesh Volumes form. If you

Apply the meshing specifications without selecting the Mesh option, GAMBIT

applies the currently specified mesh parameters to the volume(s) but does not

create the mesh.



Remove old mesh Option

If you select the Remove old mesh option, GAMBIT removes any currently

existing mesh from the specified volume(s) before creating the new volume

mesh(es). GAMBIT also enables the Remove lower mesh option (see below), which specifies whether or not to remove the mesh on the volume boundary

faces and edges. If you do not select the Remove lower mesh option, GAMBIT

retains the existing lower-topology mesh(es) when meshing the volume.

Remove lower mesh Option

As noted above, when you select the Remove old mesh option, GAMBIT

enables the Remove lower mesh option, which allows you to specify whether or not to remove any existing mesh(es) on the boundary faces and edges of the

volume(s) to be meshed.

• If you select the Remove lower mesh option, GAMBIT removes any

existing boundary face or edge meshes before remeshing the volume

(unless they are associated with other meshed topology)..

• If you do not select the Remove lower mesh option, GAMBIT retains

the existing boundary face and edge mesh(es) when remeshing the

volume.

Ignore size functions Option


size function specifications that would otherwise affect the volume mesh.



Using the Mesh Volumes Form

To open the Mesh Volumes form (see below), click the Mesh command button

on the Mesh/Volume subpad.

The Mesh Volumes form contains the following options and specifications.

Volumes � specifies the volume(s) to be meshed.

Scheme: —————————————————————————

�� Apply specifies that the meshing scheme indicated on the option

button is applied to all currently picked volumes.

Default resets the meshing scheme option button to its default algo-

rithm value (Undetermined).

Elements: ————————————————————————

Hex � Hex/Wedge Tet/Hybrid

specifies the types of elements to be used in meshing

the volume(s).



Type: ————————————————————————

Map � Submap Tet Primitive Cooper Stairstep TGrid Hex Core (Native) Hex Core (TGrid)

specifies the type of meshing scheme to apply to the

volume(s).

Smoother: (Map meshing scheme only)

None � Hilg-Wht

specifies the algorithm used to smooth the volume mesh

while meshing.

Sources � (Cooper meshing scheme only) specifies source faces for the Cooper scheme.

�� Meshed S.F. on B.L. cap

(TGrid meshing scheme only) applies a meshed size function

to any boundary layer cap. The meshed size function is

defined by two input parameters:

• Growth rate

• Max. size

(NOTE: This option is not affected by the Ignore size functions option in the lower part of the Mesh Volumes form.)

Offset layers (Hex Core (Native) meshing scheme only) specifies the number of layers of outer mesh elements to be removed

when creating the hex core.

�� Quad surface split

(Hex Core (Native) meshing scheme only) specifies that all quadrilateral mesh elements on the outer boundaries of the

hex core are split when creating the core.

�� Allow hanging nodes

(Hex Core (Native) meshing scheme only) allows the creation of hanging nodes when creating the mesh.

Peel layers (Hex Core (TGrid) meshing scheme only) specifies the number of layers of outer mesh elements to be removed

when creating the hex core.



Buffer layers (Hex Core (TGrid) meshing scheme only) specifies the number of buffer layers to use for the Hex Core (TGrid) scheme.

Size limit (Hex Core (TGrid) meshing scheme only) specifies the size limit for hex-core elements. The Size limit option includes two suboptions:

• Auto—Uses the Spacing:Interval size value as the size limit

• Manual—Uses a user-defined size limit

Spacing: —————————————————————————

�� Apply specifies that the current mesh node spacing parameters are

applied to all currently specified volume(s).

Default resets the mesh node spacing parameters to their default

values.


ing parameters.


specifies the measurement unit for the mesh node spacing

parameters.

Options —————————————————————————

�� Mesh specifies that a new mesh is created in the specified

volume(s).


specifies the removal of any current mesh that is associated

with the specified volume(s) and created by means of the

Mesh Volumes form.


specifies that all lower-topology (face and edge) meshes

associated with the specified volume(s) are removed when

the volume mesh is removed unless they are associated

with other meshed topology.





specifications that would otherwise affect the volume mesh.

(NOTE: This option does not affect the operation of the

Meshed S.F. on B.L. cap option for the TGrid meshing

scheme.)



3.4.2 Smooth Volume Meshes

The Smooth Volume Meshes operation (volume smooth command)

smoothes the spacing of mesh nodes throughout one or more volumes. When

you smooth a volume mesh, GAMBIT automatically adjusts mesh node loca-

tions in order to improve the uniformity of spacing between nodes throughout

the mesh. To smooth a volume mesh, you must specify the following para-

meters:

• The volume for which the mesh is to be smoothed

• The smoothing scheme

Specifying the Smoothing Scheme

GAMBIT provides the following mesh smoothing schemes:

• Length-weighted Laplacian (L-W Laplacian)

• Equipotential (Equipotential)

The following table summarizes the basic features of the algorithms employed

by each scheme.

Algorithm Features

Length-weighted Laplacian Uses the average edge length of the elements

surrounding each node

Equipotential Adjusts node locations to equalize the vol-

umes of the mesh elements surrounding each

node



Using the Smooth Volume Meshes Form

To open the Smooth Volume Meshes form (see below), click the Smooth Mesh command button on the Mesh/Volume subpad.

The Smooth Volume Meshes form contains the following options and specifi-

cations.

Volumes � specifies the volume(s) for which the mesh is to be smoothed.

Scheme —————————————————————————

L-W Laplacian � Equipotential

specifies the mesh smoothing algorithm. (For a general

description of each algorithm, see “Specifying the

Smoothing Scheme,” above.)



3.4.3 Set Volume Element Type

The Volume Element Type operation (default set command for the

MESH.NODES.HEX default variable) specifies the number of mesh nodes and

the node pattern associated with any of four available volume element shapes.

To set the volume element type, you must specify the numbers of nodes asso-

ciated with each of the volume element shapes. There are four volume ele-

ment shapes available in GAMBIT:

• Hexahedron

• Wedge

• Tetrahedron

• Pyramid

Every volume element shape is associated with as many as five different node

patterns. Each node pattern is characterized by the number of nodes in the

pattern. The node patterns associated with each volume element shape are as

follows:

Shape Numbers of Nodes

Hexahedron 8, 20, 27

Wedge 6, 15, 18

Tetrahedron 4, 10

Pyramid 5, 13, 14

When you set a volume element type, GAMBIT applies the specified mesh

node pattern to all volume elements of the specified shape. For example, if

you specify 20-node wedge volume elements, GAMBIT locates mesh nodes

according to the 20-node pattern for all wedge volume elements produced in

the subsequent volume meshing operation.

Figure 3-118, Figure 3-119, Figure 3-120, and Figure 3-121 show the place-

ment of nodes for each of the node patterns listed above.




(c) 27 node

= Node on element edge

= Node on element face

= Node in element center

Figure 3-118: Hexahedron volume element node patterns


(c) 18 node



Figure 3-119: Wedge volume element node patterns





Figure 3-120: Tetrahedron volume element node patterns


(c) 14 node



Figure 3-121: Pyramid volume element node patterns



Using the Set Volume Element Type Form

To open the Set Volume Element Type form (see below), click the Set Volume Element Type command button on the Mesh/Volume subpad.

The Set Volume Element Type form contains the following specifications.

Hexahedron specifies the hexahedron volume element type: 8 node, 20 node, or 27 node.

Wedge specifies the wedge volume element type: 6 node, 15 node, or 18 node.

Tetrahedron specifies the tetrahedron volume element type: 4 node or 10 node.

Pyramid specifies the pyramid volume element type: 5 node, 13 node, or 14 node.



3.4.4 Link/Unlink Volume Meshes

The Link/Unlink Volume Meshes command button allows you to perform the



Link Volume Meshes Creates hard links between volumes

Unlink Volume Meshes Deletes hard links between volumes





Link Volume Meshes

The Link Volume Meshes operation (volume link command) creates a hard

link between two volumes. When you mesh a volume that is hard-linked to

another volume, GAMBIT applies identical mesh parameters to both volumes.

� NOTE: When you select a volume for the Link Volume Meshes operation, GAMBIT automatically highlights the graphic display of any volumes to

which the volume is currently linked.

The volumes to be linked must satisfy the following criteria:

• They must be topologically identical to each other.

• The corresponding faces of each volume must be hard-linked to each

other prior to execution of the Link Volume Meshes command.

As an example of the second criterion listed above, consider the two cylindri-

cal volumes shown in Figure 3-122. The volumes are topologically identical

and differ from each other geometrically only with respect to their cross-

sectional dimensions.

volume.1 volume.2

face.2

face.3

face.1

face.5

face.6face.4

Figure 3-122: Example volumes to be hard-linked



To create a hard link between the two volumes, you must first create hard

links between face.1 and face.4, face.2 and face.5, and face.3 and face.6. (For instructions on the creation of hard links between faces, see “Link Face

Meshes,” in Section 3.3.6, above.)

Using the Link Volume Meshes Form

To open the Link Volume Meshes form (see below), click the Link command

button on the Mesh/Volume subpad.

The Link Volume Meshes form contains the following specifications.

Volume � specifies the first of two volumes to be hard-linked.

Link With —————————————————————————

Volume � specifies the second of the two volumes to be hard-linked.



Unlink Volume Meshes

The Unlink Volume Meshes operation (volume unlink command) deletes

hard mesh links associated with one or more volumes.

� NOTE: When you select a volume for the Unlink Volume Meshes operation, GAMBIT automatically highlights the graphic display of any volumes to

which the volume is currently linked.

Using the Unlink Volume Meshes Form

To open the Unlink Volume Meshes form (see below), click the Unlink com-

mand button on the Mesh/Volume subpad.

The Unlink Volume Meshes form contains the following options and specifica-

tions.

Volumes � specifies the volumes between which the link is to be deleted.

�� Lower topology

unlinks all lower-topology entities that are associated with the

specified volumes.



3.4.5 Modify Meshed Volume

The Modify Meshed Volume operation (volume split edgenodes com-

mand) converts mesh edges on the exterior faces of a meshed volume to

topological edges and creates faceted faces where appropriate. For a descrip-

tion of the procedures and specifications involved in creating a conversion list,

see “Modify Meshed Face,” in Section 3.3.7, above.

� NOTE: When GAMBIT executes the Modify Meshed Volume command, the

original meshed volume is deleted.

Using the Modify Meshed Volume Form

To open the Modify Meshed Volume form (see below), click the Modify Meshed Volume command button on the Mesh/Volume subpad.

For a general description of the procedures and specifications involved in

using the Modify Meshed Volume form, see “Using the Modify Meshed Face

Form,” in Section 3.3.7, above.



3.4.6 Summarize/Check Volume Meshes

The Summarize/Check Volume Meshes command button lets you to perform

the following operations.


Summarize Volume Mesh Summarizes general volume mesh

information in the Transcript window

Check Volume Meshes Displays 3-D mesh quality informa-

tion in the Transcript window





Summarize Volume Mesh

The Summarize Volume Mesh operation (volume msummarize command)

displays volume mesh information in the Transcript window and allows you to highlight specific mesh nodes and/or mesh elements in the graphics window.

(NOTE: For a general description of the GAMBIT mesh summary functional-

ity, see “Summarize Face Mesh,” in Section 3.3.8, above.)

Using the Summarize Volume Mesh Form

To open the Summarize Volume Mesh form (see below), click the Summarize command button on the Mesh/Volume subpad.

For a description of the use of the Summarize Volume Mesh form, see “Using

the Summarize Face Mesh Form,” in Section 3.3.8, above.



Check Volume Meshes

The Check Volume Meshes operation (volume check quality command)

displays 3-D mesh quality data. When you execute the Check Volume Meshes command, GAMBIT displays the following information elements in the

Transcript window:

• A table that summarizes 3-D mesh quality statistical information for

all volumes specified on the Check Volume Meshes form

• A summary statement that includes the numbers of specified volumes

that contain highly skewed and inverted elements

Tabular 3-D Mesh Quality Data

The Check Volume Meshes tabular output represents the statistical distribution of element mesh quality values for the current default 3-D quality metric.

Table 3.2 shows an example of such output for a volume mesh evaluated

according to the EquiAngle Skew quality metric. Output such as that shown in

Table 3.2 constitutes a numerical representation of the mesh quality histogram

that is displayed on the Examine Mesh form when you choose the Display Type:Range option (see Section 3.4.2 of the GAMBIT User’s Guide).

Table 3.2: Example Check Volume Meshes tabular output

Summarizing EQUIANGLE SKEW of 3D elements for 1 meshed volume:

Volume volume.1 meshed using Map scheme and size of 1.000000.

From value To value Count in range % of total count (1463)

--------------------------------------------------------------

0 0.1 286 19.55

0.1 0.2 671 45.86

0.2 0.3 341 23.31

0.3 0.4 88 6.02

0.4 0.5 66 4.51

0.5 0.6 11 0.75

0.6 0.7 0 0.00

0.7 0.8 0 0.00

0.8 0.9 0 0.00

0.9 1 0 0.00

--------------------------------------------------------------

0 1 1463 100.00

In addition to the tabular output shown in Table 3.2, the Check Volume Meshes command displays the minimum and maximum values of element quality for

the set of specified volumes. The minimum and maximum element quality

information is not available by means of any other GAMBIT operation.



Specifying the Quality Metric

As noted above, the Check Volume Meshes command evaluates mesh element

quality according to the current default 3-D mesh quality metric. To change

the metric used to evaluate element quality for the Check Volume Meshes com-

mand, you must modify the default 3-D mesh quality metric by means of the

Edit Defaults form. To do so:


2. Click the MESH tab to open the MESH defaults subform.

3. Select the EXAMINE radio button to display the EXAMINE variables.

4. Modify the ELEMENT_3D_QUALITY variable.

(For a complete description of the procedures required to modify default vari-

ables by means of the Edit Defaults form, see Section 4.2.4 of the GAMBIT

User’s Guide.)

For example, to evaluate 3-D elements on the basis of the Aspect Ratio metric:

1. Use the procedure described above to set Aspect Ratio as the default

quality metric (ELEMENT_3D_QUALITY=2 )

2. Execute the Check Volume Meshes command.

� NOTE: Check Volume Meshes command tabular output, such as that shown in

Table 3.2, includes all 3-D elements that possess shapes for which the current

default quality metric applies. For example, if you specify EquiAngle Skew as the default 3-D quality metric, the tabular output includes all hexahedral,

tetrahedral, prism, and wedge elements associated with the volumes specified

on the Check Volume Meshes form. However, if you specify Aspect Ratio as the default 3-D quality metric, the tabular output includes only hexahedral and tet-

rahedral elements, because the Diagonal Ratio metric does not apply to prism or

wedge elements.



Summary Statement

The Check Volume Meshes summary statement indicates the number of speci-

fied volumes that “fail” the mesh check for skewed and inverted elements—

for example,

0 out of 1 meshed volume failed mesh check for skewed elements (>.98).

0 out of 1 meshed volume failed mesh check for inverted elements.

In the context of the Check Volume Meshes command, any volume that

includes at least one inverted mesh element fails the mesh check.

Using the Check Volume Meshes Form

To open the Check Volume Meshes form (see below), click the Check com-


The Check Volume Meshes form contains the following specification.

Volumes � specifies the volumes for which mesh element quality is to be

evaluated.



3.4.7 Delete Volume Meshes

The Delete Volume Meshes operation (volume delete onlymesh com-

mand) deletes the mesh from one or more volumes. When you delete a

volume mesh, GAMBIT allows you to retain or delete all face meshes and

edge meshes associated with the volume.

Using the Delete Volume Meshes Form

To open the Delete Volume Meshes form (see below), click the Delete com-


The Delete Volume Meshes form contains the following options and specifica-

tions.

Volumes � specifies the volume(s) for which the mesh is to be deleted.

All � Pick

• All specifies all volumes in the model.

• Pick specifies volumes selected by means of the

Volumes list box.


removes all unused lower-topology meshes associated with

the specified volume(s).

Group Meshing Commands CREATING THE GEOMETRY


3.5 Group Meshing Commands

The following commands are available on the Mesh/Group subpad.


Mesh Groups Creates a mesh for all components of

a group

Summarize Group Meshes Check Group Meshes

Summarizes general group mesh

information; summarizes group mesh

quality information

Delete Group Meshes Deletes the mesh from groups

The following sections describe the purpose and operation of each of the com-

mands listed above.

CREATING THE GEOMETRY Group Meshing Commands


3.5.1 Mesh Groups

The Mesh Groups operation (group mesh and group modify commands)

activates meshing operations for one or more groups of topological entities.

Overview

When you mesh a group by means of the Mesh Groups command, GAMBIT

performs meshing operations for all of the topological entities that comprise

components of the group. If you apply meshing parameters to any or all com-

ponents of the group prior to executing the Mesh Groups command, GAMBIT

meshes those components according to their previously applied parameters.

All other components of the group are meshed according to the default mesh-

ing parameters. For example, if you mesh a group that includes three edges to

one of which has been previously applied a double-sided, successive-ratio

grading scheme, GAMBIT honors the applied scheme when it meshes the

group but meshes the other two edges according to the current default grading

scheme.

Group Meshing Parameters

To perform a group meshing operation, you must specify the following

parameters:

• Group name(s)


The group name(s) parameter specifies the name of one or more existing

groups the components of which are to be meshed. The mesh node spacing

parameter specifies the number of edge mesh intervals that are to be created

on all edges for which a grading scheme has not been previously applied.

For a description of the mesh node spacing specifications, see “Specifying

Node Spacing,” in Section 3.2.1.



Using the Mesh Groups Form

To open the Mesh Groups form (see below), click the Mesh command button

on the Mesh/Group subpad.

The Mesh Groups form includes the following specifications.

Groups � specifies the group(s) to be meshed.

Spacing —————————————————————————

�� Apply specifies that the current mesh node spacing parameter is

applied to all components of the group.

Default resets the mesh node spacing parameter to its default

values.


ing parameter.


specifies the unit definition of the mesh node spacing

parameter.

Options —————————————————————————

�� Mesh specifies that a new mesh is created for the specified

group(s).


specifies the deletion of any current mesh that is associated

with the specified group(s) and created by means of the

Mesh Groups form.




specifies that all lower-topology (volume, face, and edge)

meshes associated with the specified group(s) are deleted.



3.5.2 Summarize/Check Group Meshes

The Summarize/Check Group Meshes command button lets you to perform the



Summarize Group Meshes Summarizes general group mesh

information in the Transcript window

Check Group Meshes Displays mesh quality information in

the Transcript window





Summarize Group Meshes

The Summarize Group Meshes operation (group msummarize command)

displays in the Transcript window mesh summary information for all topo-

logical entities that comprise the components of a group.

Using the Summarize Group Meshes Form

To open the Summarize Group Meshes form (see below), click the Summarize command button on the Mesh/Group subpad.

The Summarize Group Meshes form contains the following options and speci-

fications.

Groups � specifies the group for which summary information is dis-

played in the Transcript window.



Check Group Meshes

The Check Group Meshes operation (group check quality command)

displays mesh quality data for entities associated with specified groups. When

you execute the Check Group Meshes command, GAMBIT displays the fol-

lowing items in the Transcript window:

• Tables that summarize 2-D and 3-D mesh quality statistical informa-

tion for all faces and volumes associated with the specified group(s)

• Summary statements that include the numbers of inverted 2-D or 3-D

elements as well as the numbers of specified faces and volumes in the

specified group(s) that contain inverted mesh elements

Tabular Mesh Quality Data

The Check Group Meshes tabular outputs represent the statistical distributions of element mesh quality values for the current default 2-D and 3-D quality

metrics. For descriptions of the information contained in such outputs, as well

as the procedures for specifying the quality metrics, see Sections 3.3.8 and

3.4.6 in this guide.

Summary Statement

The Check Group Meshes summary statements indicate the numbers of faces

and/or volumes in the specified group(s) that “fail” the mesh check. In the

context of the Check Group Meshes command, any face or volume that

includes at least one inverted mesh element fails the mesh check.

Using the Check Group Meshes Form

To open the Check Group Meshes form (see below), click the Check command

button on the Mesh/Group subpad.

The Check Group Meshes form contains the following specification.

Groups � specifies the groups for which mesh element quality is to be

evaluated.



3.5.3 Delete Group Meshes

The Delete Group Meshes operation (group delete onlymesh command)

removes the mesh from all topological entities that comprise components of

one or more groups.

When you delete the mesh for one or more groups, GAMBIT allows you to

delete all meshes that are associated with the lower-topology of the group

components. To delete the mesh associated with such components, select the

Remove lower unused mesh option on the Delete Group Meshes form.

As an example of the effect of the Remove lower unused mesh option, con-sider a group (group.1) that contains only a single volume (volume.1) and a single, separate face (face.7).

• If you delete the mesh from group.1 and select the Remove lower unused mesh option, GAMBIT deletes all vertex, edge, face, and vol-

ume meshes associated with volume.1 and face.7.

• If you delete the mesh from group.1 and do not select the Remove lower unused mesh option, GAMBIT deletes the volume mesh from volume.1 but retains all vertex, edge, and face meshes associated with volume.1. Likewise, GAMBIT deletes the face mesh from face.7 entity but retains all vertex and edge meshes associated with face.7.



Using the Delete Group Meshes Form

To open the Delete Group Meshes form (see below), click the Delete command

button on the Mesh/Group subpad.

The Delete Group Meshes form includes the following specifications.

Groups � specifies the groups containing topological entities from which

the mesh is to be removed.

All � Pick

• All specifies all groups in the model.

• Pick specifies groups selected by means of the Groups list box.


deletes all unused lower-topology meshes that are associ-

ated with the specified group(s).

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