Godunov型CSPM方法

CSPM方法是传统SPH方法的改进,它有效地解决了传统SPH方法在求解含边界问题时的困难。然而最近研究表明,CSPM方法在求解含间断算例时却存在计算不稳定的问题。本文基于Godunov间断分解思想和CSPM方法提出了Godunov型CSPM方法。该方法成功地解决了CSPM在求解含间断流体学问题中遇到的困难,且不用引入人工粘性。为了验证算法的有效性,本文采用一维激波管算例对不同方法进行了对比计算。计算结果表明,本文提出的方法比以往SPH方法有更高的间断捕获精度。

Godunov-type corrective smoothed particle method (CSPM)

The CSPM(Corrective Smoothed Particle Method) is developed from standard SPH(Smoothed Particle Hydrodynamics) Method,which improves the standard SPH in solving the boundary deficiency problem.But recent research indicated its faulty in simulation the problem which contains discontinuity.A new method named Godunov-type CSPM is proposed and the 1-Dimentional Godunov-type CSPM formulation is deduced in this paper,which combines CSPM with Godunov method seamlessly and overcomes the wrong position capture of shockwave caused by asymmetric CSPM discrete formulations.This new approach improves the CSPM when solving the discontinuous phenomena of fluid dynamics with no artificial viscosity required.Moreover,numerical test on a classical 1-Dimensional Sod shock tube problem was carried out to examine the performance of the new method,and the result shows that the new method improves shockwave capture,but worsen the accuracy in expand wave comparing with other SPH method.