基于移动网格的熵稳定格式

计算物理 ›› 2017, Vol. 34 ›› Issue (2): 175-182.

基于移动网格的熵稳定格式

程晓晗^1,2, 聂玉峰², 蔡力², 封建湖¹

1. 长安大学理学院, 陕西西安 710064;
2. 西北工业大学应用数学系, 陕西西安 710129

收稿日期:2016-01-13 修回日期:2016-05-19 出版日期:2017-03-25 发布日期:2017-03-25
作者简介:程晓晗(1987-),男,安徽枞阳,博士,讲师,从事计算流体力学方法研究,E-mail:xhcheng@chd.edu.cn
基金资助:
国家自然科学基金（11601037，11401045，11471261）和中央高校基本科研业务费专项资金（310812171002）资助项目

Entropy Stable Scheme Based on Moving Meshesfor Hyperbolic Conservation Laws

CHENG Xiaohan^1,2, NIE Yufeng², CAI Li², FENG Jianhu¹

1. School of Science, Chang'an University, Xi'an 710064, China;
2. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China

Received:2016-01-13 Revised:2016-05-19 Online:2017-03-25 Published:2017-03-25

摘要/Abstract

摘要： 提出一种基于移动网格的熵稳定格式求解双曲型守恒律方程.该方法利用等分布原理得到新的网格分布，基于守恒型插值公式计算新的网格上的物理量，使用熵稳定数值通量和三阶强稳定Runge-Kutta时间推进方法得到下一时刻的数值解.数值算例表明该格式不仅能有效提高解在间断处的分辨率，而且能消除可能产生的伪振荡.

关键词: 双曲守恒律, 熵稳定格式, 移动网格方法, 熵守恒, 数值耗散

Abstract: An entropy stable scheme based on moving meshes is proposed for hyperbolic conservation laws. The method employs equidistribution principle to redistribute mesh points. Numerical solutions on new meshes are updated by using a conservative-interpolation formula. Entropy stable fluxes and third order strong stability-preserving Runge-Kutta time evolution method are employed to obtain numerical solutions at next time level. Several test problems are presented to demonstrate that the method not only improves resolution in discontinuous areas, but also reduces possible spurious oscillations.

Key words: hyperbolic conservation laws, entropy stable scheme, moving mesh method, entropy conservation, numerical diffusion operator

中图分类号:

O354
O241.82

程晓晗, 聂玉峰, 蔡力, 封建湖. 基于移动网格的熵稳定格式[J]. 计算物理, 2017, 34(2): 175-182.

CHENG Xiaohan, NIE Yufeng, CAI Li, FENG Jianhu. Entropy Stable Scheme Based on Moving Meshesfor Hyperbolic Conservation Laws[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(2): 175-182.

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