Mapped WENO schemes based on a new smoothness indicator for Hamilton-Jacobi equations

被引：9

作者：

Ha, Youngsoo ^{[2
]}

Kim, Chang Ho ^{[3
]}

Lee, Yeon Ju ^{[4
]}

Yoon, Jungho ^{[1
]}

机构：

[1] Ewha W Univ, Dept Math, Seoul 120750, South Korea

[2] Natl Inst Math Sci, Taejon 305811, South Korea

[3] Konkuk Univ, Dept Comp Engn, Chungju 380701, South Korea

[4] Ewha W Univ, Inst Math Sci, Seoul 120750, South Korea

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 394卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

WENO schemes; Mapped WENO schemes; Smoothness indicators; Hamilton-Jacobi equations; Level set; ESSENTIALLY NONOSCILLATORY SCHEMES; SEMIDISCRETE CENTRAL SCHEMES; SHOCK-CAPTURING SCHEMES; WEIGHTED ENO SCHEMES; VISCOSITY SOLUTIONS; EFFICIENT IMPLEMENTATION; CONSERVATION-LAWS; SYSTEMS;

D O I：

10.1016/j.jmaa.2012.04.040

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce an improved version of mapped weighted essentially non-oscillatory (WENO) schemes for solving Hamilton-Jacobi equations. To this end, we first discuss new smoothness indicators for WENO construction. Then the new smoothness indicators are combined with the mapping function developed by Henrick et al. (2005) [31]. The proposed scheme yields fifth-order accuracy in smooth regions and sharply resolve discontinuities in the derivatives. Numerical experiments are provided to demonstrate the performance of the proposed schemes on a variety of one-dimensional and two-dimensional problems. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：670 / 682

页数：13

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