Stability of Newton TVD Runge-Kutta scheme for one-dimensional Euler equations with adaptive mesh

被引：15

作者：

Yuan, Xinpeng ^{[1
]}

Ning, Jianguo ^{[1
]}

Ma, Tianbao ^{[1
]}

Wang, Cheng ^{[1
]}

机构：

[1] Beijing Inst Technol, State Key Lab Explos Sci & Technol, Beijing 081, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2016年 / 282卷

基金：

中国国家自然科学基金;

关键词：

Euler equations; Adaptive mesh; Stability; Newton TVD Runge-Kutta; EQUIDISTRIBUTION; REFINEMENT; SYSTEMS;

D O I：

10.1016/j.amc.2016.02.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose a moving mesh method with a Newton total variation diminishing (TVD) Runge-Kutta scheme for the Euler equations. Our scheme improves time discretization in the moving mesh algorithms. By analyzing the semi-discrete Euler equations with the discrete moving mesh equations as constraints, the stability of the Newton TVD Runge-Kutta scheme is proved. Thus, we can conclude that the proposed algorithm can generate a weak solution to the Euler equations. Finally, numerical examples are presented to verify the theoretical results and demonstrate the accuracy of the proposed scheme. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：1 / 16

页数：16

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