SPH方法和MPS方法模拟溃坝问题的比较分析

Comparative study of SPH and MPS methods for numerical simulations of dam breaking problems

SPH(Smoothed Particle Hydrodynamics)方法和MPS(Moving Particle Semi-Implicit)方法是两种常用的无网格粒子法,在处理自由面大变形问题方面有较大的灵活性,然而这两种方法在数值格式、计算效率和收敛性等方面有许多不同之处。本文以二维溃坝问题为例对SPH方法和MPS方法进行了比较分析,结果表明:SPH方法易于给出更为清晰、光滑的自由面形状,而MPS方法给出的粒子分布较为凌乱;在收敛性上,随着初始粒子间距的减小,SPH和MPS均趋于收敛,但MPS方法收敛得更快些;对于时间步长,在满足CFL条件且计算稳定的情况下,对结果影响不是很大;在计算效率上,SPH方法具有较高的效率,适合求解大型复杂流动问题,而MPS方法计算量较大。通过对SPH方法和MPS方法的比较分析,为具体问题计算选用不同的无网格粒子方法提供了选择依据。

SPH（Smoothed Particle Hydrodynamics） and MPS（Moving Particle Semi-Implicit） are two commonly used Lagrangian particle methods.They have excellent flexibility in dealing with large-deformed free surface flows.But there are some differences between SPH and MPS on numerical scheme,computational efficiency,and speed of convergence.A 2-D dam breaking problem is chosen to be simulated by the SPH and MPS to investigate these two methods in this paper,the numerical results show that the profile of water by the SPH is usually clearer and smoother,while those obtained by the MPS present a splashing and violent free surface.In addition,convergence is investigated in this paper,the results show that suitable large particle number is essential to capture the details of flow,and the convergence rate of the MPS is quicker than that of the SPH as the initial space distance between neighboring particles decreasing.The adopted time step doesn＇t make too much effect on the results when the CFL condition is satisfied.For computational efficiency,the SPH is more efficient in dealing with large-scale free surface flows while the MPS method is very time-consuming to solve linear system equations.Through the investigation,we provide a basis for selection of different meshless particle methods for specific problem.