随机选取法和多波近似在一维浅水方程大时间步长格式中的应用

计算物理 ›› 2013, Vol. 30 ›› Issue (5): 649-658.

随机选取法和多波近似在一维浅水方程大时间步长格式中的应用

许仁义, 钟德钰, 吴保生

水沙科学与水利水电工程国家重点实验室, 清华大学水利水电工程系, 北京 100084

收稿日期:2012-12-20 修回日期:2013-04-11 出版日期:2013-09-25 发布日期:2013-09-25
作者简介:许仁义(1980-),男,博士生,主要研究方向为水动力计算,E-mail:xry08@mails.tsinghua.edu.cn
基金资助:
国家973项目(2011CB409901);国家自然科学基金(51039004)资助项目

LTS in Shallow Flows with RCM and Multi-wave Approximation

XU Renyi, ZHONG Deyu, WU Baosheng

Department of Hydraulic Engineering, Tsinghua University, Beijing 100086, China

Received:2012-12-20 Revised:2013-04-11 Online:2013-09-25 Published:2013-09-25

摘要/Abstract

摘要： 利用黎曼精确解和行波法相结合,在一维浅水方程中实现大时间步长(Large Time Step,LTS)格式,并采用多波近似解决稀疏波断裂的问题,采用随机选取法(Random Choice Method,RCM)解决非线性方程使用LTS格式出现的震荡问题.一系列数值试验发现,通过多波近似和随机选取法对大时间步长格式的改进,提高了计算效率,减小了震荡,取得了很好的计算效果.

关键词: 随机选取法, 多波近似, 大时间步长格式, 浅水方程

Abstract: Exact Riemann solver and wave propagation method are combined to achieve large time-step scheme (LTS) in shallow water flow. Multi-wave approximation is adapted to solve discontinuity of rarefaction, and a random choice method (RCM) is used to eliminate oscillation in nonlinear hyperbolic systems. Efficiency is increased in LTS scheme with multi-wave approximation and random choice method as large Courant-Fridrichs-Lewy (CFL) number is imposed.

Key words: random choice method (RCM), multi-wave approximation, large-time step (LTS) scheme, shallow water equations

中图分类号:

许仁义, 钟德钰, 吴保生. 随机选取法和多波近似在一维浅水方程大时间步长格式中的应用[J]. 计算物理, 2013, 30(5): 649-658.

XU Renyi, ZHONG Deyu, WU Baosheng. LTS in Shallow Flows with RCM and Multi-wave Approximation[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 30(5): 649-658.