Single-Step Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for 1-D Euler Equations

作     者：Jayesh Badwaik Praveen Chandrashekar Christian Klingenberg Jayesh Badwaik;Praveen Chandrashekar;Christian Klingenberg

作者机构：Department of MathematicsUniversity of WürzburgWürzburgGermany TIFR Center for Applicable MathematicsBangaloreIndia 

出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)

年 卷 期：2020年第2卷第4期

页      面：541-579页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Airbus Foundation TIFR-CAM Deutsche Forschungsgemeinschaft, DFG 

主　　题：Discontinuous Galerkin method Moving meshes Arbitrary Lagrangian-Eulerian Euler equations 

摘      要：We propose an explicit,single-step discontinuous Galerkin method on moving grids using the arbitrary Lagrangian-Eulerian approach for one-dimensional Euler *** grid is moved with the local fluid velocity modified by some smoothing,which is found to con-siderably reduce the numerical dissipation introduced by Riemann *** scheme preserves constant states for any mesh motion and we also study its positivity preservation *** grid refinement and coarsening are performed to maintain the mesh qual-ity and avoid the appearance of very small or large ***,higher order methods are developed and several test cases are provided to demonstrate the accuracy of the proposed scheme.