CFD simulations using an AMR-like approach in the PDE Framework Peano
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1 CFD simulations using an AMR-like approach in the PDE Framework Peano, Fakultät für Informatik Technische Universität München Germany Miriam Mehl, Hans-Joachim Bungartz, Takayuki Aoki
2 Outline PDE Framework Peano Vision & Motivation Features Adaptive Simulation Results Integration of higher-order IDO into Peano
3 Peano - Vision Computational challenges Multi-scale in time Multi-scale in space Multi-physics Techniques Complex/changing geometries & solution behaviour: dynamic (local) adaptivity Geometric multigrid solver Computational demands: parallelisation via domain decomposition Approach Cartesian grids Space-filling curves Stack data structures
4 Peano - Features Framework for different applications (Poisson, NSE, etc.): plug-in concept Cartesian grids Regular (lexicographic) Adaptive (spacetree)
5 Peano - Features Space-filling curves (Peano): Seralisation of the adaptive grid (parallelisation + load balancing) Recursive construction fits to spacetree grid construction Allow for high cache-hit rates (>98%): Temporal locality Spatial locality (with stacks)
6 Peano - Features Stack data structures Spatial locality!
7 CFD in Peano: Adaptive Simulation Results incompressible Navier-Stokes equations Semi-implict approach Low-order FEM (Q1P0) Pressure Poisson Equation (PETSc) Time-integration: Explicit Euler Benchmark scenario: Laminar channel flow around a cylinder A lot of reference data available 1) Lift and drag forces for comparison Re = 20 1) S. Turek and M. Schaefer, Benchmark Computations of Laminar Flow around a Cylinder Vieweg, Notes on Numerical Fluid Mechanics 52, 1996
8 Adaptive Simulation Results lmax = 8 lmin = 5
9 Adaptive Simulation Results lmax = 9 lmin = 7
10 Integration of IDO into Peano Lid-driven cavity (NSE), IDO-CF Regular grid Runge-Kutta Operators cell-wise! Temporary data: 2 Vectors per node 1 Vector per face Re=1000, 50x50 cells
11 Summary & Outlook Peano: Suitable framework for PDE simulations on adaptive Cartesian grids Stacks + SFC: performance + changing geometries Integration of higher order schemes directly feasible Ongoing work: Dynamic adaptivity criteria 3D simulations with moving geometries (such as FSI) Performance tuning Parallelisation Geometric multigrid
12 Thanks for your attention!
13 Backup Adaptive Grid cells
14 Backup II Cylinder Benchmark 3D cells
15 Problem for PDE solver: Peano Motivation - raus??? storage usage => loss of efficiency Solution: cache hierarchy on modern computer architectures Our approach: Cartesian grids (spacetree) + space-filling curves + stacks
16 Integration of IDO into Peano Continuity equation Unit square [0,1] 2 Periodic boundary conditions Regular grid Runge-Kutta time integration Operators: cell-wise! t=0 t=0.4 t=0.7 t=1
17 Backup III 3D adaptive Drift-Ratchet
18 Backup IV Peano Architecture
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