Comparison of different iterative schemes for ISPH based on Rankine source solution
Comparison of different iterative schemes for ISPH based on Rankine source solution
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DOI：
10.1016/j.ijnaoe.2016.10.007
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发表时间：
2017-07
影响因子：
2.2
通讯作者：
Xing Zheng;Q. Ma;W. Duan
中科院分区：
文献类型：
--
作者：
Xing Zheng;Q. Ma;W. Duan
光滑粒子流体力学（SPH）方法对自由表面流动问题的模拟具有良好的适应性。SPH有两种形式。一个是弱可压缩SPH，另一个是不可压缩SPH （ISPH）。与前一种方法相比，ISPH方法在许多情况下具有更好的性能。基于Rankine源解的ISPH由于避免了压力泊松方程的二阶导数，可以使用更大的步长，比传统的ISPH性能更好。然而，ISPH_R方法需要求解压力泊松方程的稀疏线性矩阵，这是一次步进计算中最昂贵的部分之一。求解大粒子数泊松方程通常采用迭代法。然而，有许多可用的迭代方法，使用哪一种的问题仍然是开放的。本文比较了CGS、Bi-CGstab和GMRES三种适合求解大型非对称稀疏矩阵的迭代方法。通过静水试验、溃坝、水塘剧烈晃动、孤立波撞击等不同情况下的数值试验，表明GMRES方法比CGS和Bi-CGstab方法更有效。
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.