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