3 computational models

8/22/2019 3 Computational Models

1/10

Computer ModellingBuilding Computational Models


2/10

Computer Modelling

2

Steps In Computational ModellingBuild Geometry

(CAD)

Mesh theGeometry

Visualize theresults

Solve governingequations

CAD generates geometry. CAD domain broken down into

small elements - meshing

Number of methods used todiscretise equations as solvertechnology:

Finite Difference Finite Element Finite Volume

Graphical packages availablefor visualisation.


3/10

Computer Modelling

3

GeometryHow well does the computer represent the real world?

CAD software often used at this stage check veracity of the arising

geometrical model.

Are we capturing all the important details?


4/10

Computer Modelling

4

Material Properties and behaviour

How do my materials behave?

Stress in Solder Joints (Elastic or Plastic)Stress in Substrates (Isotropic or Orthotropic)Air flow through a heat sink (Laminar or Turbulent)

How accurate is my materials data?

Youngs Modulus (Temperature dependent)Fluid Viscosity.


5/10

Computer Modelling

5

Boundary + Initial Conditions

Am I using the correct boundary conditions?

Inlet flow rate at a fan.Power source in a chip.

Boundary Conditions

DirichletNeumannMixed

Initial Conditions

Flotherm Prediction of Temperature


6/10

Computer Modelling

6

Analysis TypeCan I assume the domain is 2-dimensional?

Is my analysis dependent on time?

Steady state analysisTransient Analysis

Can I avoid non-linearities in the analysis?

Elastic material properties (Linear) - easierPlasticity (Non-Linear) more solution effort

y

x


7/10

Computer Modelling

7

Building Models

For example consider the temperature, u(x,y), across the following plate.

Mathematical model to represent temperature u(x,y) is:

x

yInsulated

Insulated

100oC

25oC

(0,0)

(10,5)

Solve :

2

u

x 2+

2

u

y 2= 0.0, 0 < x < 10, 0 < y < 5

Subject to : (BC)u

y(x, 0) = u

y(x, 5) = 0.0 0 x 10

u (0,y) = 25 u (10,y) = 100 0 < y < 5


8/10

Computer Modelling

8

Building Models

u(

10,y

)=100

u(0,y

)=25

MODEL RESULT

Insulated

Insulated

100oC

25oC

(0,0)

(10,5)

REAL WORLD


9/10

Computer Modelling

9

Meshing Structured and Unstructured

Data referenced using I,J grid linesLow in-core memory requirementPoor on complex shapes.

- Use Block-Structured.

Good for complex geometryTopology representation

- Points - Faces - Elements

Mix element types.Requires whole field solvers.

- Large memory needed.


10/10

Computer Modelling

10

Mesh QualityThe shape of the elements making up the mesh should be of reasonable quality

Poor elements with large aspect ratios and internal angles

Mesh quality depends on analysis type most codes have internal checks.

Good Poor

3 computational models

Documents