一种非结构网格上求解拉格朗日形式可压缩欧拉方程的二阶RKDG方法  

A Second-Order RKDG Method for Lagrangian Compressible Euler Equations on Unstructured Triangular Meshes

作　　者：赵晓龙 邱美兰 蔚喜军[3] 卿芳 邹世俊 Zhao Xiaolong;Qiu Meilan;Yu Xijun;Qing Fang;Zou Shijun(Beijing Computational Science Research Center,Graduate School of China Academy of Engineering Physics,Beijing 100193;School of Mathematics and Statistics,Huizhou University,Guangdong Huizhou 516007;Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,Beijing 100088)

机构地区：[1]中国工程物理研究院研究生院北京计算科学研究中心,北京100193 [2]惠州学院数学与统计学院,广东惠州516007 [3]北京应用物理与计算数学研究所,北京100088

出　　处：《数学物理学报（A辑）》2020年第5期1354-1361,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金(11571002,11772067,11702028,U1930402);广东省自然科学基金(2018A030310038);中国工程物理研究院基金(CX2019032)。

摘　　要：该文结合间断Galerkin(DG)方法和拉格朗日格式,提出了一种非结构三角网格上求解拉格朗日形式可压缩欧拉方程的二阶Runge-Kutta(RK)DG方法.相比其它需要考虑拉格朗日空间和欧拉空间之间的映射雅可比矩阵的纯拉格朗日格式,该方法更加简洁,并且方法的顶点速度求解器对许多算例都有很好的适应性.数值算例展示了方法的鲁棒性和二阶精度.This paper takes advantages of the Discontinuous Galerkin(DG)method and Lagrangian scheme to present a second-order Runge-Kutta(RK)DG method for solving Lagrangian compressible Euler equations on unstructured triangular meshes.The method is more succinct than other fully Lagrangian schemes with the Jacobian matrix associated with the map between Lagrangian and Eulerian spaces,the solver of vertex velocity in the method has good adaptability for many problems.Numerical examples are presented to illustrate the robustness and second-order accuracy of the scheme.

关 键 词：拉格朗日格式 非结构三角网格 RKDG方法 

分 类 号：O241.82[理学—计算数学]