High-order weighted compact nonlinear scheme for one- and two-dimensional Hamilton-Jacobi equations

被引：5

作者：

Jiang, Yan-Qun ^{[1
]}

Zhou, Shu-Guang ^{[2
]}

Zhang, Xu ^{[1
]}

Hu, Ying-Gang ^{[1
]}

机构：

[1] Southwest Univ Sci & Technol, Dept Math, Mianyang, Sichuan, Peoples R China

[2] China Aerodynam Res & Dev Ctr, Mianyang, Sichuan, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2022年 / 171卷 / 353-368期

基金：

中国国家自然科学基金;

关键词：

High-order schemes; WCNS; Hamilton-Jacobi equations; WENO-Z; High resolution; ESSENTIALLY NONOSCILLATORY SCHEMES; SEMIDISCRETE CENTRAL SCHEMES; FINITE-ELEMENT-METHOD; HERMITE WENO SCHEMES; TIME DISCRETIZATIONS; VISCOSITY SOLUTIONS;

D O I：

10.1016/j.apnum.2021.09.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper designs a fifth-order weighted compact nonlinear scheme (WCNS) on a five-point stencil to solve one-and two-dimensional Hamilton-Jacobi equations. The five-point WCNS is used to compute the left and right limits of first-order spatial derivatives of the HJ equations in the Lax-Friedrichs monotone numerical Hamiltonian. The WENO-Z type interpolation for cell-edge values of the solutions is used to suppress numerical oscillations which may appear near discontinuities. Five-and seven-point WENO-Z schemes for Hamilton-Jacobi equations are also designed for comparisons. The performance of the WCNS and the two WENO-Z schemes is demonstrated by several numerical examples in one-dimensional and two-dimensional cases. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：353 / 368

页数：16

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