二维浅水波方程的数值激波不稳定性

计算物理 ›› 2012, Vol. 29 ›› Issue (1): 25-35.

二维浅水波方程的数值激波不稳定性

沈智军^1,2, 胡立军³, 闫伟¹

1. 北京应用物理与计算数学研究所计算物理实验室, 北京 100088;
2. 北京大学应用物理与技术研究中心, 北京 10087l;
3. 中国工程物理研究院研究生部, 北京 100088

收稿日期:2011-03-18 修回日期:2011-05-27 出版日期:2012-01-25 发布日期:2012-01-25
作者简介:沈智军(1966-),男,辽宁,博士,研究员,从事计算流体力学方法研究
基金资助:
国家自然科学基金(11071025);国防基础科研项目(B1520110011);中物院科学技术发展基金(2010A0202010);计算物理实验室基金资助项目

Numerical Shock Instability for 2-D Shallow Water Equations

SHEN Zhijun^1,2, HU Lijun³, YAN Wei¹

1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
2. Center for Applied Physics and Technology, Peking University, Beijing 100871, China;
3. Graduate School of China Academy of Engineering Physics, Beijing 100088, China

Received:2011-03-18 Revised:2011-05-27 Online:2012-01-25 Published:2012-01-25

摘要/Abstract

摘要： 研究二维浅水波方程的数值激波不稳定性问题.线性稳定性分析和数值实验表明,格式的临界稳定性与数值激波的不稳定现象有重要的联系.基于扰动量的增长矩阵分析,本文将高分辨率的数值格式和HLL格式进行特定的加权,设计一类新的混合型数值格式.其中可以调节非线性波速的HLLC与HLL的混合格式,数值试验展示了消除浅水波方程激波不稳定现象的有效性和鲁棒性.

关键词: 激波不稳定性, 浅水波方程, 线性稳定性分析, 混合通量格式

Abstract: In calculation of multidimensional fluid mechanics problems with numerical schemes that accurately capture contact discontinuity, perturbation near shock wave may increase dramatically. This is called numerical shock instability. In this paper numerical shock instability on shallow water equations is studied. By analyzing linear stability of several numerical schemes, marginal stability of schemes are found having close relation with numerical shock instability. According to eigenvalue analysis, a hybrid method is designed to remedy nonphysical phenomenon by locally modify the original schemes. Numerical experiments show efficiency and robustness of HLLC-HLL hybrid scheme in eliminating shock instability of shallow water equations.

Key words: numerical shock instability, shallow water equations, analysis of linear stability, hybrid method

中图分类号:

O241

沈智军, 胡立军, 闫伟. 二维浅水波方程的数值激波不稳定性[J]. 计算物理, 2012, 29(1): 25-35.

SHEN Zhijun, HU Lijun, YAN Wei. Numerical Shock Instability for 2-D Shallow Water Equations[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 29(1): 25-35.