Corrected SPH methods for solving shallow-water equations

作     者：陈善群 廖斌 黄涛 Shan-qun CHEN;Bin LIAO;Tao HUANG

作者机构：College of Architecture and Civil Engineering Anhui Polytechnic University 

出 版 物：《Journal of Hydrodynamics》 (水动力学研究与进展B辑（英文版）)

年 卷 期：2016年第28卷第3期

页      面：389-399页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：Project supported by the National Natural Science Foun-dation of China(Grant No.51175001) the Natural Science Foundation of Anhui Province(Grant No.1508085QE100) the Higher Education of Anhui Provincial Scientific Research Project Funds(Grant No.TSKJ2015B03) 

主　　题：smoothed particle hydrodynamics (SPH) methodology artificial viscosity Lax-Friedrichs flux two-shock Riemannsolver MUSCL reconstruction shallow water equations 

摘      要：The artificial viscosity in the traditional smoothed particle hydrodynamics （SPH） methodology concerns some empirical coefficients, which limits the capability of the SPH methodology. To overcome this disadvantage and further improve the accuracy of shock capturing, this paper introduces two other ways for numerical viscosity, which are the Lax-Friedrichs flux and the two- shock Riemann solver with MUSCL reconstruction to provide stability. Six SPH methods with different kinds of numerical viscosity are tested against the analytical solution for a 1-D dam break with a wet bed. The comparison shows that the Lax-Friedrichs flux with MUSCL reconstruction can capture the shock wave more accurate than other five methods. The Lax-Friedrichs flux and the artificial viscosity with MUSCL reconstruction are finally both applied to a 2-D dam-break test case in a L-shaped channel and the numerical results are compared with experimental data. It is concluded that this corrected SPH method can be used to solve shallow-water equations well.