TAU mesh deformation

Thomas Gerhold

The parallel mesh deformation of the DLR TAU-Code

Introduction

Mesh deformation method & Parallelization

Results & Applications

Conclusion & Outlook

CFD needs mesh deformation to account for changes of the geometry shape

e.g. in

simulations for fluid structure interaction

or shape optimisation procedures or …

Introduction

Mesh deformation adjusts the coordinates of the interior grid points according to the surface displacements given as input.

This avoids expensive re-meshing and minimises grid dependencies of the solution due to constant grid connectivity.

The mesh deformation problem

The problem is: how to move the interior grid points such that the grid remains valid.

The surface displacements are most often much larger than the local cell sizes. As a result it is a non-trivial task to avoid collapsing of cells.

For unstructured meshes usually strategies are employed, which are based on

spring analogy (tension or torsion) or linear elasticity equations. The computational costs are not negligible.

Sufficient robustness for 3D complex geometries is questionable. The literature does not provide the optimal solution (for fine NS grids for 3D complex geometries! 2D or Euler grids or coarse NS grids are not the problem)

Mesh deformation method of the TAU-Code

An alternative mesh deformation method has been developed for the TAU Code.

It is an algebraic method, which is fast and robust for many applications.

The TAU-Code is employed routinely in parallel on distributed memory architectures. Grids of 10 million points (and often more) are distributed typically over 16, 32 or 64 processors (sometimes more).

This requires a parallel mesh deformation, which works on the same grid partitions as the flow solver:

to avoid memory bottlenecks on single computational nodes.

to profit from a parallel speed up.

The algebraic mesh deformation method

Basic principle of the method:

Algebraic prolongation of the giveninput displacements into the interiorof the grid.

Compute interior displacementsby averages from neighbour points in the backward layer

Consider translation and rotationof points in the backward layer for avoiding skew cells and increasingrobustness

Mesh deformation

test for mesh deformation with rotation of points:

A rotated mesh and a deformed mesh for which the rotation is given only on the deformation surface are compared.

Mesh deformationThe algebraic method is based on an advancing front algorithm.

Advancing front methods are not well suited for parallelization.

parallel set up:

1 step: advance the front per partition in the interior of the grid

2 step: communicate displacements on grid overlap

repeat step 1 and 2 till updates remain unchanged

Advancing the front has to be repeated

(typically) 30 to 50 times in parallel mode

partition 1

partition 2partition 3

partition overlap

deformation surface

interior grid

How to build the advancing front?

The order in which interior points are updated influences the result.

The shape of an advancing front of cell layers is strongly influenced by different cell sizes.

the front originated on the fuselage (small or zero displacements) wraps around the outer wing, where typically are the largest displacements

How to build the front alternatively?

How to build the advancing front?

Making the prolongation of displacements independent of local cell sizes

1) sort interior grid points by distance to the initial deformation surface

2) update interior displacements in a loop over the sorted points

each point update requires only data of neighbour points which have a smaller distance and which are thus already updated. As a result one single loop over all points is required only.

How to compute step 1 in order to make the algorithm highly efficient?

loop over all points, check for each ( ) if a neighbour point ( ) has a surface coordinate which is nearer than its own: if yes, take it

repeat till no more point gets an update

If the points are suitable sorted usually 15 to 20 sweeps are needed only (less than 10 seconds for one million grid points on a modern PC )

already updatedactual point in loop

How to compute the distance to the deformation surface for interior points efficiently in parallel?

deformation surface

In parallel mode,

communicate surface coordinates on grid partition boundaries after each sweep (increases the number of sweeps by a factor of 3 or 4).

Limit of the deformation method

The described method is able to handle small and some times also medium size deformations. If the deformations become too large the first cells of the grid start to collapse.

wing tip deformation 120collaped tetras 3collapseds prisms 0

wing tip deformation 240collaped tetras 383collapseds prisms 149

wing tip deformation 360collaped tetras 712collapseds prisms 238

wing tip deformation 540collapsed tetras 1463collapsed prisms 470

Hybrid mesh for DLR F6N-tetras ~ 3400000N-prisms ~ 3600000N-points ~ 2500000

outer chord length ~60span of wing ~580

The capability of repairing some hundred collapsed elements only,increases the robustness of the mesh deformation method considerably

collapsed elements

How to repair elementsinitial grid

extract boundaryof the valid part of

the grid

optionally extend this region

extract the same boundary in the initial grid

computetransformation

matrix

apply transformation on points of collapsed

elements

Its a volume splineapplied locally in

regions containing collapsed cells

deformed grid withcollapsed cells

Grid repair: results

span of the wing

outer chord length

realistic range

.

For unsteady applications using large numbers of processes the costs of the deformation can be become remarkable.

This is due to the non load balanced occurrence of collapsed cells and their local repair

wing tip deflection 240(4 outer chord length)

Parallel efficiency

Memory scales with the number of processes (not shown here)

For static aeroelasticsimulations (call deformation each 500 iteration) runtime of deformation is negligible.

Timings for the main algorithmic parts of the deformation on a 2 GHz Opteron dual core cluster.

F6 GRID for WBPN3.75 million points, 4.88 million tetrahedra, 5.7 million prisms.

Limits of the deformation method – they depends on the initial grid quality

Grid for A380with 2m wing tip deflectionpoints 1.0 * 107

tetras 1.0 * 107

prisms 1.5 * 107

pyras 5.0 * 104

collapsed tets 5

top view

side view

deformation

Deformation can become impossible if elements are too flat in relation to the deformation size.

Limits of the deformation method – they depend on the initial grid quality

Problems with collapsing elements seem to occure due to chopping of prism-layers such that high aspect ratio prisms are connected to flat tetras.

For those cases we do not have a solution available yet.

Aeroelastic applications (by J. Neumann)

Procedure for the following dynamic aeroelastic simulations

temporal coupling

conventional serial staggered scheme CSS

spatial coupling: radial basis functions for interpolation between CSM & CFD surfaces

Flap-Wing & AMP wing: infinite plate spline

X31: volume spline

structure:

NASTRAN eigenvalue analysis to obtain mass and stiffness matrices

equation of motion solved with Newmark scheme (structural damping neglected)

start

1 Step: steady converged solution with non-deformed mesh

2 Step: compute response of structure & apply deformations per time step

Dynamic aeroelasticity for wing-flap model

Test for deformation of chimera grids:

angle of attack α=0.0°; Flap angle Φ=0°; Onflow Ma=0.5

Start from undeformedconverged steady statesolution

200 time steps; ∆t=0.01s; change of flap angle from Φ=0°to 10° in the first 100 time steps, afterwards constant flapdeflection

AMP-Wing – Unsteady simulation - TAU-Nastran

Ma=0.60 TAU-Euler-CFDMa=0.82 TAU-URANS-CFD

AMP Wing: 3-D flutter simulation near transonic dipTAU-Code Navier/Stokes coupled with NASTRAN

LCO for AMP: p0=1,1 bar; Ma=0.82; α=2,55°

FE-modell of X-31-wind tunel model

generic CSM-model for large deformations

geometry based on CFD surface datamodel consists of shell elements (CQUAD4 und TRIA3)model consists of 279 nodes and 312 elements

CFD-surface mit 168935 surface points,

9.6 millionelements, 1.7 million points

FE-model with 819 degrees of freedom

X-31: half-model with sharp leading edgeα=16.0°; Mach=0.4; ∆t=0.0005 s; p=100000 N/m²

Displacement vectors on finite element model (left) and deformations at wing tipand canard tip over the time (rechts)

Conclusion & outlook

The parallel TAU deformation method

has been described and demonstrated, it is robust for many applications.

can be applied on the same grid partitions distributed over the processes for the TAU preprocessor/solver and adaptation, without re-partitioning and redistribution of data.

the memory requirements scale with the number of processes, thus it is no memory bottleneck for large scale applications.

the time requirements of the parallel deformation for static aeroelasticsimulations are negligible.

for dynamic aeroelastic simulations the runtime requirements of the parallel deformation can become relevant (> 25% of solver runtime).

Improvements or alternative methods might have to be considered, especially for massive parallel applications.

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