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

6. Correction and Consistance ——advanced topic …

7. Lists of kernel function Cubic spline2h2h Quartic spline2.5h Fifth order B-spline3h3h Truncated Gaussian

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

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

10. Boundary Condition Sym: ghost particles, Free surface, p 0 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-box Parallel Sparse Matrix Solver SPH Method Lagrangian Method Large deformation Continue changing domain Complex domain structure Why not Domain decomposition ? 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 Parallel Sparse symmetric positive definite matrix Direct solver or Iterative solver

14. ColoringColoring 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 MPS Parallel Strategy: OpenMP Almost linear speedup

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

25. 3D Cavity Flow: Re=400 Yang Jaw-Yen et al. 1998 J. Comput. Phys. 146:464-487 45 X 45 X 45 nodes h/dx=1.5

29. 3D Dambreaking Tests Kleefsman, K.M.T. et al 2005 J. Comput. Phys. 206:363-393

32. 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.