线性传输方程的Entropy-Monotone格式

上海交通大学学报（自然版） ›› 2016, Vol. 50 ›› Issue (05): 810-813.

线性传输方程的Entropy-Monotone格式

王志刚1,2，崔艳芬2

(1.阜阳师范学院数学与统计学院，安徽阜阳 236037; 2.上海大学理学院，上海 200444)

收稿日期:2015-04-13 出版日期:2016-05-28 发布日期:2016-05-28
基金资助:
国家自然科学基金（1141104；11301328），中国博士后科学基金（2015M581579）资助项目

EntropyMonotone Scheme for Linear Advection Equation

WANG Zhigang1,2,CUI Yanfen2

(1. School of Mathematics and Statistics, Fuyang Normal College, Fuyang 236037, Anhui, China; 2. School of Sciences, Shanghai University, Shanghai 200444, China)

Received:2015-04-13 Online:2016-05-28 Published:2016-05-28

摘要/Abstract

摘要： 摘要：在守恒律方程组的数值计算中，线性间断的磨损问题备受关注.为了减少线性间断的磨损，针对线性传输方程，提出了EntropyMonotone格式.该格式属于Godunov型格式，包括重构、发展和求网格平均3个步骤.与传统的Godunov格式不同，该格式同时计算数值解和数值熵，并通过它们构造分片常数的台阶函数.数值实验表明，此格式对线性间断的模拟非常有效.

关键词: 线性传输方程, Godunov格式, EntropyMonotone格式

Abstract: Abstract： In numerical computation of conservation laws, the problem of the wear of linear discontinuity is of great concern. In order to decrease the wear of linear discontinuity, an entropymonotone scheme was designed for the linear advection equation. This scheme is a Godunov scheme, which includes reconstruction, evolution, and cellaveraging. Different from the traditional Godunov scheme, this scheme simultaneously computes the numerical solution and numerical entropy, and uses them to reconstruction the “step function” in each cell. Numerical experiments show that this scheme is very effective for the simulation of linear discontinuity.

Key words: Key words： linear advection equation, Godunov scheme, EntropyMonotone scheme

中图分类号:

O 241.82

王志刚1,2，崔艳芬2. 线性传输方程的Entropy-Monotone格式[J]. 上海交通大学学报（自然版）, 2016, 50(05): 810-813.

WANG Zhigang1,2,CUI Yanfen2. EntropyMonotone Scheme for Linear Advection Equation[J]. Journal of Shanghai Jiaotong University, 2016, 50(05): 810-813.

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