Simulating complex surface flow by Smoothed Particle Hydrodynamics

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

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

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

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

expression of derivatives W’ W 0 h 1. 3 ~ 1. 5 Integral Summation Trapeze like quadrature formula 3. 0 2 h 130+ (2 D)

Correction and Consistance ——advanced topic …

Lists of kernel function Cubic spline 2 h Quartic spline 2. 5 h Fifth order B-spline 3 h Truncated Gaussian

Hydrodynamics governing equations SPH: weakly compressible method: State Equation Ma < 0. 1 MPS: projection method: Pressure Poisson Equation

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

Boundary Condition • Sym: ghost particles, • Free surface, p 0 Identify the surface particle: 95% const. density

Large Scale Computation (a few millions particles) share memory architecture (NEC SX 8: 8 nodes, 128 G RAM) (Dell T 5400: 2 Quad cores Xeon 16 G RAM) • SPH – Particle lists partition, NOT domain partition • MPS – parallel ICCG method

Black-box Parallel Sparse 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…

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

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.

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 2 h T. Iwashita & M. Shimasaki 2002 IEEE Trans. Magn. The connection info could be obtained from the distribution of non-zeros in the sparse matrix

bcsstk 14 n=1806, nnz=63454

MC=50 MC=180

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

SPH Parallel Strategy: Open. MP Almost linear speedup MPS Parallel Strategy: Open. MP

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

Dambreaking Test Surge front location

Water entry of a wedge 4. 5 M particles Speed up around 7 Dell T 5400 2 Xeon Quadcores

3 D Cavity Flow: Re=400 45 X 45 nodes Yang Jaw-Yen et al. 1998 J. Comput. Phys. 146: 464 -487 h/dx=1. 5

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

0. 6 MARIN Exp. Results Water Level (m) 0. 5 H 4 H 3 H 2 H 1 0. 4 0. 3 0. 2 SPH Results 0. 1 0. 0 0. 5 1. 0 Time (s) 1. 5 2. 0

Conclusions • 2 D code is developed for both SPH and MPS methods • 3 D 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.