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Simulating complex surface flow by S moothed P article H ydrodynamics & M oving P article S emi-implicit metho

Simulating complex surface flow by S moothed P article H ydrodynamics & M oving P article S emi-implicit methods. Benlong Wang Kai Gong Hua Liu benlongwang@sjtu.edu.cn S hanghai Jiaotong University . Contents. Introduction SPH & MPS methods

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Simulating complex surface flow by S moothed P article H ydrodynamics & M oving P article S emi-implicit metho

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  1. Simulating complex surface flow by Smoothed Particle Hydrodynamics& Moving Particle Semi-implicit methods Benlong Wang Kai Gong Hua Liu benlongwang@sjtu.edu.cn Shanghai Jiaotong University

  2. Contents • Introduction • SPH & MPS methods • Parallel strategy and approaches • SPH: • MPS: • Numerical results • 2D dam breaking • 2D wedge entry • 3D cavity flow • 3D dam breaking

  3. Modeling free surface flows • Multiphase flows: MAC, VOF, LevelSet etc. • ALE • Meshless methods & particle methods SPH & MPS LBM

  4. Kernel function • Properties: • Narrow support • decreases monotonously as increase • h->0, Dirac delta function h dx W

  5. 0 expression of derivatives W W’ h 1.3 ~ 1.5 Integral Summation 3.0 2h 130+ (2D) Trapeze like quadratureformula

  6. Correction and Consistance——advanced topic … ? ?

  7. Lists of kernel function

  8. Hydrodynamics governing equations SPH: weakly compressible method: State Equation Ma < 0.1 MPS: projection method: Pressure Poisson Equation

  9. Link-List neighbour search L SPH: the most time consuming part ~90% back ground mesh (L X L) L=2h, 3h, support distance MPS: generally less than PPE solver

  10. Boundary Condition • Sym: ghost particles, • Free surface, p0 Identify the surface particle: 95% const. density

  11. Large Scale Computation(a few millions particles)share memory architecture(NEC SX8: 8 nodes, 128G RAM)(Dell T5400: 2 Quad cores Xeon 16G RAM) • SPH • Particle lists partition, NOT domain partition • MPS • parallel ICCG method

  12. Black-boxParallelSparse Matrix Solver Why not Domain decomposition ? SPH Method Lagrangian Method Large deformation Continue changing domain Complex domain structure So, Black-box solver give me a matrix, I will solve it in parallel…

  13. PPE solver : ICCG method • Precondition ILU(0) • Forward and backward substitutions • Inner products • Matrix-vector products • Vector updates Direct solver or Iterative solver Sparse symmetric positive definite matrix Parallel

  14. Coloring • COLOR: Unit of independent sets. • Any two adjacent nodes have different colors. Elements grouped in the same “color” are independent from each other, thus parallel/vector operation is possible. • Many colors provide faster convergence, but shorter vector length.

  15. Main Idea of the Coloring Algebraic Multi-Color Ordering The number of the colors has a lower boundary the max bandwidth of the sparse matrix  Any two adjacent nodes have different colors 2h T. Iwashita & M. Shimasaki 2002 IEEE Trans. Magn. The connection info could be obtained from the distribution of non-zeros in the sparse matrix

  16. bcsstk14 n=1806,nnz=63454

  17. MC=50 MC=180

  18. Parallelized ICCG with AMC Forward and backward substitutions: parallelized in each color

  19. SPH Parallel Strategy: OpenMP Almost linear speedup MPS Parallel Strategy: OpenMP

  20. Numerical Results • 2D dam breaking • 2D wedge water entry • 3D cavity flow • 3D dam breaking

  21. Dambreaking Test Surge front location

  22. Water entry of a wedge 4.5M particles Speed up around 7 Dell T5400 2 Xeon Quadcores

  23. 3D Cavity Flow: Re=400 45 X 45 X 45 nodes h/dx=1.5 Yang Jaw-Yen et al. 1998 J. Comput. Phys. 146:464-487

  24. 3D Dambreaking Tests Kleefsman, K.M.T. et al 2005 J. Comput. Phys. 206:363-393

  25. 0.6 H4 H3 MARIN Exp. Results H2 0.5 H1 0.4 Water Level (m) 0.3 SPH Results 0.2 0.1 0.0 0.0 0.5 1.0 1.5 2.0 Time (s)

  26. Conclusions • 2D code is developed for both SPH and MPS methods • 3D code is developed for complex free surface flows • Computation costs of SPH is generally cheaper than MPS method • Good agreements are obtained, a promising method for complex free surface flows.

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