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Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids

Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids. Miriam Mehl Ionel Muntean, Tobias Neckel, Tobias Weinzierl Computer Science TU München. Why Cartesian Grids?. Numerical Efficiency. hierarchically structured Cartesian grids arbitrarily local adaptivity

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Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids

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  1. Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Miriam Mehl Ionel Muntean, Tobias Neckel, Tobias Weinzierl Computer Science TU München Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  2. Why Cartesian Grids? Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  3. Numerical Efficiency • hierarchically structured Cartesian grids • arbitrarily local adaptivity • full approximation schemes • efficient multigrid methods Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  4. Hardware Efficiency ½ ½ -1 • cell-oriented operator evaluation • constant difference stencils • no neighbour relations • low storage Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  5. Hardware Efficiency • Peano curve • processing order of grid cells • time locality of data access Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  6. Hardware Efficiency • stacks as data structures • spatial locality of data access Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  7. Hardware Efficiency • cache-misses 110% of minimum • runtime 5 times DiMe (regular grid) 3D Poisson • sphere, adaptive • 23,118,848dofs Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  8. Flexibility • geometric adaptivity • Eulerian approach (marker-and-cell) • complicated changing geometries Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  9. Accuracy • geometric adaptivity • cutting-cell methods • hierarchical operator generation • second order accuracy in geometry Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  10. Physical Correctness • Verstappen, 2001: • symmetry requirements • energy and momentum conservation FEM: Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  11. Physical Correctness • FEM-basis: u-v-coupled, piecewise linear • correct velocity interpolation • dynamical adaptivity, coupling surface Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  12. Why Cartesian Grids? Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  13. Numerical Results • Regular grid code F3F: • symmetry preserving FV discretisation • fully parallel • full 3D functionality • platforms up to now: • HLRB2 (SGI Altix 4700) • TU München Infinicluster (128 CPU Opteron) • Universität Stutgart Mozart (128 CPU Xeon cluster) Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  14. Numerical Results Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  15. Numerical Results • Adaptive grid code Peano: • 2D Navier-Stokes • parallel Poisson • platforms up to now: • HLRB2 (SGI Altix 4700) • TU München Infinicluster (128 CPU Opteron) • PC cluster Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  16. Numerical Results • Free channel flow: Re=1111 • in preparation to DNS • boundary layer: adaptively refined Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

  17. Conclusion + Outlook • appropriateness of our approach • concept for adaptive grids: Navier-Stokes • Cartesian grids: applications • next steps: • fully functional 3D parallel adaptive NS-solver • refinement criteria for turbulent boundary layers • runtime optimisation on supercomputers Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

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