A Study on CFL Conditions for the DG Solution of Conservation Laws on Adaptive Moving Meshes

作     者：Min Zhang Weizhang Huang Jianxian Qiu 

作者机构：School of Mathematical SciencesPeking UniversityBeijing 100871China Department of MathematicsUniversity of KansasLawrenceKansas 66045USA School of Mathematical SciencesFujian Provincial Key Laboratory of Mathematical ModelingHigh-Performance Scientific ComputingXiamen UniversityXiamenFujian 361005China 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2023年第16卷第1期

页      面：111-139页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：M.Zhang was partially supported by the Postdoctoral Science Foundation of China(Grant 2022M710229) J.Qiu was partially supported by National Natural Science Foundation of China(Grant 12071392) 

主　　题：Discontinuous Galerkin method adaptive mesh moving mesh CFL condition stability 

摘      要：The selection of time step plays a crucial role in improving stability and efficiency in the Discontinuous Galerkin(DG)solution of hyperbolic conservation laws on adaptive moving meshes that typically employs explicit stepping.A commonly used selection of time step is a direct extension based on Courant-Friedrichs-Levy(CFL)conditions established for fixed and uniform *** this work,we provide a mathematical justification for those time step selection strategies used in practical adaptive DG computations.A stability analysis is presented for a moving mesh DG method for linear scalar conservation *** on the analysis,a new selection strategy of the time step is proposed,which takes into consideration the coupling of theα-function(that is related to the eigenvalues of the Jacobian matrix of the flux and the mesh movement velocity)and the heights of the mesh *** analysis also suggests several stable combinations of the choices of theα-function in the numerical scheme and in the time step *** results obtained with a moving mesh DG method for Burgers’and Euler equations are *** comparison purpose,numerical results obtained with an error-based time step-size selection strategy are also given。