Comparison of different iterative schemes for ISPH based on Rankine source solution

• Published in: International journal of naval architecture and ocean engineering 2017, 9(4), , pp.390-403
• Main Authors: Zheng, Xing, Ma, Qing-wei, Duan, Wen-yang
• Format: Article
• Language: English
• Subjects: Dam breaking; ISPH; ISPH_R; Iterative scheme; Solitary wave slamming; SPH; Violent tank sloshing; 조선공학
• ISSN: 2092-6782; 2092-6790
• DOI: 10.1016/j.ijnaoe.2016.10.007

Smoothed Particle Hydrodynamics (SPH) method has a good adaptability for the simulation of free surface flow problems. There are two forms of SPH. One is weak compressible SPH and the other one is incompressible SPH (ISPH). Compared with the former one, ISPH method performs better in many cases. ISPH based on Rankine source solution can perform better than traditional ISPH, as it can use larger stepping length by avoiding the second order derivative in pressure Poisson equation. However, ISPH_R method needs to solve the sparse linear matrix for pressure Poisson equation, which is one of the most expensive parts during one time stepping calculation. Iterative methods are normally used for solving Poisson equation with large particle numbers. However, there are many iterative methods available and the question for using which one is still open. In this paper, three iterative methods, CGS, Bi-CGstab and GMRES are compared, which are suitable and typical for large unsymmetrical sparse matrix solutions. According to the numerical tests on different cases, still water test, dam breaking, violent tank sloshing, solitary wave slamming, the GMRES method is more efficient than CGS and Bi-CGstab for ISPH method.