Finite Volume HWENO Schemes for Nonconvex Conservation Laws

被引：5

作者：

Cai, Xiaofeng ^{[1
]}

Qiu, Jianxian ^{[2
,3
]}

Qiu, Jingmei ^{[1
]}

机构：

[1] Univ Houston, Dept Math, Houston, TX 77204 USA

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

[3] Xiamen Univ, Fujian Prov Key Lab Math Modeling & High Performa, Xiamen 361005, Fujian, Peoples R China

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2018年 / 75卷 / 01期

基金：

美国国家科学基金会;

关键词：

Nonconvex conservation laws; Finite volume HWENO scheme; Entropy solution; Entropic projection; HERMITE WENO SCHEMES; DISCONTINUOUS GALERKIN METHOD; ESSENTIALLY NONOSCILLATORY SCHEMES; HAMILTON-JACOBI EQUATIONS; RIEMANN-PROBLEM; LIMITERS;

D O I：

10.1007/s10915-017-0525-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Following the previous work of Qiu and Shu (SIAM J Sci Comput 31: 584-607, 2008), we investigate the performance of Hermite weighted essentially non-oscillatory (HWENO) scheme for nonconvex conservation laws. Similar to many other high order methods, we show that the finite volume HWENO scheme performs poorly for some nonconvex conservation laws. We modify the scheme around the nonconvex regions, based on a first order monotone scheme and a second entropic projection, to ensure entropic convergence. Extensive numerical tests are performed. Compare with the earlier work of Qiu and Shu which focuses on 1D scalar problems, we apply the modified schemes (both WENO and HWENO) to one-dimensional Euler system with nonconvex equation of state and two-dimensional problems.

引用

页码：65 / 82

页数：18

共 20 条

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