Technische Universität München Benefits of Structured Cartesian Grids for the Simulation of Fluid- Structure Interactions Miriam Mehl Department of Computer.

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Presentation transcript:

Technische Universität München Benefits of Structured Cartesian Grids for the Simulation of Fluid- Structure Interactions Miriam Mehl Department of Computer Science TU München

Technische Universität München Outline Our Cartesian Grids Requirements Fluid-Structure Interactions Cartesian Grids – CFD Cartesian Grids – Coupling Application Examples Conclusion

Technische Universität München Our Cartesian Grids Cartesian grid cells  squares/cubes recursive refinement  tree structure

Technische Universität München Our Cartesian Grids Cartesian grid cells  squares/cubes recursive refinement  tree structure

Technische Universität München Fluid-Structure Interactions – Requirements complex and changing geometries  flow solver

Technische Universität München Fluid-Structure Interactions – Requirements complex and changing geometries  flow solver partitioned approaches  coupling of codes  modularity Structure Solver Flow Solver Coupling

Technische Universität München Cartesian Grids – CFD fast and flexible geometry treatment Eulerian Approach + Marker-and-Cell

Technische Universität München Cartesian Grids – CFD # grid cellsruntime (sec) 52,662, ,666, , Pentium 4, 2.4 GHz, 512 MB cache fast and flexible geometry treatment

Technische Universität München Cartesian Grids – CFD fast and flexible geometry treatment

Technische Universität München Cartesian Grids – CFD fast and flexible geometry treatment

Technische Universität München Cartesian Grids – CFD recursive cell-tree  local grid changes fast and flexible geometry treatment

Technische Universität München Cartesian Grids – CFD hardware + numerical efficiency

Technische Universität München Cartesian Grids – CFD cell-oriented operator evaluation  constant difference stencils  no neighbour relations

Technische Universität München Cartesian Grids – CFD cell-oriented operator evaluation  constant difference stencils  no neighbour relations i,j i-1,j ½ -1 ½

Technische Universität München Cartesian Grids – CFD cell-oriented operator evaluation  constant difference stencils  no neighbour relations i,j i-1,j i,j i-1,j -1 ½ ½

Technische Universität München Cartesian Grids – CFD cell-oriented operator evaluation  constant difference stencils  no neighbour relations i-1,j ½ -1 ½

Technische Universität München Cartesian Grids – CFD cell-oriented operator evaluation  constant difference stencils  no neighbour relations ½ ½ -1

Technische Universität München Cartesian Grids – CFD Peano curve  linearisation of the cell-tree  processing order

Technische Universität München Cartesian Grids – CFD Peano curve  linearisation of the cell-tree  processing order

Technische Universität München Cartesian Grids – CFD Peano curve + stacks = data access with  locality in space  locality in time

Technische Universität München Cartesian Grids – CFD Peano curve + stacks = data access with  locality in space  locality in time

Technische Universität München Cartesian Grids – CFD low memory requirements bytes/cellbytes/vertex 2D 62only grid 1420flow solver 3D 102only grid 1828flow solver hardware + numerical efficiency

Technische Universität München ==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% ) Cartesian Grids – CFD 2D Poisson equation, 1,000,000 degrees of freedom, Pentium 4, 1MB L2 Cache, Cachegrind simulation hardware + numerical efficiency high cache-efficiency

Technische Universität München Cartesian Grids – CFD multigrid dehierarchisation compute residual smooth restrict residual hardware + numerical efficiency

Technische Universität München Cartesian Grids – CFD # dyn. refinem.k=0k=1k=2k=3 # iterations91099 accuracy5.972e e e e-5 Poisson equation on a cube, F-cycle hardware + numerical efficiency multigrid

Technische Universität München Cartesian Grids – CFD tol. 1.17e-3reg. gridadapt. grid # dofs hardware + numerical efficiency dynamical adaptivity

Technische Universität München Cartesian Grids – CFD dynamically balanced parallelisation

Technische Universität München Cartesian Grids – CFD  connected partitions  quasi-minimal partition surface dynamically balanced parallelisation

Technische Universität München Cartesian Grids – CFD dynamically balanced parallelisation

Technische Universität München Advantages of Cartesian Grids – CFD dynamically balanced parallelisation

Technische Universität München Cartesian Grids – CFD dynamically balanced parallelisation

Technische Universität München Cartesian Grids – Coupling efficient data mapping for non-matching grids fluid solver + interpolation struct. solver + interpolation FSI*ce surface coupling Grid administration Data mapping

Technische Universität München Cartesian Grids – Coupling

Technische Universität München Cartesian Grids – Coupling sphere (8,000 triangles)

Technische Universität München Cartesian Grids – Coupling grid resolution# boundary nodesruntime [s] 6418, , , ,227, sphere (8,000 triangles), Pentium M 1.6 GHz, 2048 kB cache efficient data mapping for non-matching grids

Technische Universität München Cartesian Grids – Coupling trianglesruntime [s] 16, , , , grid resolution 512, Pentium M 1.6 GHz, 2048 kB cache efficient data mapping for non-matching grids

Technische Universität München Application Examples – Cylinder Benchmark

Technische Universität München Application Examples – Beam

Technische Universität München Application Examples – Drift Ratchet silicon wafer pierced with pores oscillating pressure conditions suspended particles (0.1 – 1.2  m) observation: particle drift

Technische Universität München Application Examples – Drift Ratchet

Technische Universität München Application Examples – Drift Ratchet

Technische Universität München Application Examples – Drift Ratchet frequency=10kHzfrequency=14kHz

Technische Universität München Application Examples – Drift Ratchet frequency=7kHz frequency=14kHz

Technische Universität München Conclusion applicability of Cartesian Grids fast grid generation / updates memory efficiency numerical efficiency

Technische Universität München Persons Hans-Joachim Bungartz Markus Brenk Klaus Daubner Ioan Lucian Muntean Tobias Neckel Tobias Weinzierl