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

Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Why Cartesian Grids? numerical efficiency + (adaptivity, multigrid) hardware efficiency ??? (not automat.) flexibility + (adaptivity, marker and cell) accuracy physical correctness Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids 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

Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids 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

Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids 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

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

Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Hardware Efficiency cache-misses 110% of minimum runtime 5 times DiMe (regular grid) 3D Poisson sphere, adaptive 23,118,848 dofs # processes Speedup 4 3.73 8 6.85 16 12.93 Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

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

Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids 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

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

Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids 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

Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Why Cartesian Grids? numerical efficiency + (adaptivity, multigrid) hardware efficiency + (space-filling curves, stacks) flexibility + (adaptivity, marker and cell) accuracy + (adapt., cutting-cell, hier. op. Gen.) physical correctness + (divergence preserv. FE basis) Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids Computer Science, TU München

Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids 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

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

Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids 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

Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids 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

Efficient Parallel Simulation of Fluid Dynamics on Cartesian Grids 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