Technische Universität München Benefits of Structured Cartesian Grids for the Simulation of Fluid-...

Technische Universität München

Benefits of Structured Cartesian Grids for the Simulation of Fluid-

Structure Interactions

Miriam Mehl

Department of Computer Science

TU München


Outline

• Our Cartesian Grids

• Requirements Fluid-Structure Interactions

• Cartesian Grids – CFD

• Cartesian Grids – Coupling

• Application Examples

• Conclusion


Our Cartesian Grids

• Cartesian grid cells

squares/cubes

• recursive refinement

tree structure


Fluid-Structure Interactions – Requirements

• complex and changing geometries

flow solver


Fluid-Structure Interactions – Requirements

• complex and changing geometries

flow solver

• partitioned approaches

coupling of codes

modularity

Structure SolverFlow Solver

Coupling


Cartesian Grids – CFD

fast and flexible geometry treatment

Eulerian Approach + Marker-and-Cell



# grid cells runtime (sec)

52,662,337 48.188

210,666,753 168.641

842,687.105 662.797Pentium 4, 2.4 GHz, 512 MB cache




• recursive cell-tree local grid changes




hardware + numerical efficiency



cell-oriented operator evaluation

constant difference stencils

no neighbour relations






i,ji-1,j ½ -1

½






i,ji-1,j

i,ji-1,j

-1 ½½






i-1,j

i-1,j

½ -1 ½






½½ -1



Peano curve

linearisation of the cell-tree

processing order



Peano curve + stacks = data access with

locality in space

locality in time



low memory requirements

bytes/cell bytes/vertex

2D6 2 only grid

14 20 flow solver

3D10 2 only grid

18 28 flow solver



==19243== D refs: 7,249,842,728 (4,026,485,237 rd + 3,223,357,491 wr)==19243== D1 misses: 1,249,032 ( 621,413 rd + 627,619 wr)==19243== L2d misses: 632,162 ( 301,283 rd + 330,879 wr)==19243== D1 miss rate: 0.0% ( 0.0% + 0.0% )==19243== L2d miss rate: 0.0% ( 0.0% + 0.0% )==19243== ==19243== L2 refs: 19,559,185 ( 18,931,566 rd + 627,619 wr)==19243== L2 misses: 646,343 ( 315,464 rd + 330,879 wr)==19243== L2 miss rate: 0.0% ( 0.0% + 0.0% )


2D Poisson equation, 1,000,000 degrees of freedom, Pentium 4, 1MB L2 Cache, Cachegrind simulation


high cache-efficiency



multigrid

• dehierarchisation• compute residual• smooth• restrict residual




# dyn. refinem. k=0 k=1 k=2 k=3

# iterations 9 10 9 9

accuracy 5.972e-2 4.613e-3 4.521e-4 6.771e-5

Poisson equation on a cube, F-cycle


multigrid



0

)sin(3 2

u

xu i

tol. 1.17e-3 reg. grid adapt. grid

# dofs 509.656 61.267


dynamical adaptivity



dynamically balanced parallelisation

0

1 2 3 4

5 6 7 8 17 18 19 20

13 14 15 169 10 11 12



connected partitions

quasi-minimal partition surface



Advantages of Cartesian Grids – CFD




1 10 20 30 40 50 60 70 80 90 100 Row

6705

101520253035404550556065707580

Speedup



Cartesian Grids – Coupling

efficient data mapping for non-matching grids

fluid solver+ interpolation

struct. solver+ interpolation

FSI*cesurfacecoupling

Grid administration

Data mapping



sphere (8,000 triangles)



grid resolution # boundary nodes runtime [s]

64 18,482 0.200

128 75,514 0.671

256 305,394 2.594

512 1,227,987 10.114

sphere (8,000 triangles), Pentium M 1.6 GHz, 2048 kB cache




triangles runtime [s]

16,000 12.7

32,000 14.3

64,000 16.2

128,000 17.4

grid resolution 512, Pentium M 1.6 GHz, 2048 kB cache



Application Examples – Cylinder Benchmark


Application Examples – Beam


Application Examples – Drift Ratchet

• silicon wafer pierced with pores

• oscillating pressure conditions

• suspended particles (0.1 – 1.2 m)

• observation: particle drift



frequency=10kHzfrequency=14kHz



frequency=7kHz frequency=14kHz


Conclusion

• applicability of Cartesian Grids

• fast grid generation / updates

• memory efficiency

• numerical efficiency


Persons

Hans-Joachim Bungartz

Markus Brenk

Klaus Daubner

Ioan Lucian Muntean

Tobias Neckel

Tobias Weinzierl

Technische Universität München Benefits of Structured Cartesian Grids for the Simulation of Fluid-...

Documents

Transcript of Technische Universität München Benefits of Structured Cartesian Grids for the Simulation of Fluid-...