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

数学物理学报 ›› 2020, Vol. 40 ›› Issue (5): 1354-1361.

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

赵晓龙¹,邱美兰²,蔚喜军^3,*(),卿芳³,邹世俊³

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

收稿日期:2018-12-12 出版日期:2020-10-26 发布日期:2020-11-04
通讯作者: 蔚喜军 E-mail:yuxj@iapcm.ac.cn
基金资助:
国家自然科学基金(11571002);国家自然科学基金(11772067);国家自然科学基金(11702028);国家自然科学基金(U1930402);广东省自然科学基金(2018A030310038);中国工程物理研究院基金(CX2019032)

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

Xiaolong Zhao¹,Meilan Qiu²,Xijun Yu^3,*(),Fang Qing³,Shijun Zou³

¹ Beijing Computational Science Research Center, Graduate School of China Academy of Engineering Physics, Beijing 100193
² School of Mathematics and Statistics, Huizhou University, Guangdong Huizhou 516007
³ Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088

Received:2018-12-12 Online:2020-10-26 Published:2020-11-04
Contact: Xijun Yu E-mail:yuxj@iapcm.ac.cn
Supported by:
the NSFC(11571002);the NSFC(11772067);the NSFC(11702028);the NSFC(U1930402);the NSF of Guangdong Province(2018A030310038);the CAEP Foundation of China(CX2019032)

摘要/Abstract

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.

关键词: 拉格朗日格式, 非结构三角网格, RKDG方法

Abstract:

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.

Key words: Lagrange scheme, Unstructured triangular meshes, RKDG method

中图分类号:

O241.82

赵晓龙,邱美兰,蔚喜军,卿芳,邹世俊. 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[J]. 数学物理学报, 2020, 40(5): 1354-1361.

Xiaolong Zhao,Meilan Qiu,Xijun Yu,Fang Qing,Shijun Zou. A Second-Order RKDG Method for Lagrangian Compressible Euler Equations on Unstructured Triangular Meshes[J]. Acta mathematica scientia,Series A, 2020, 40(5): 1354-1361.

图/表 4

参考文献 8

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$h({\cal D}(t))$	$L^{1}$ error	order	$L^{2}$ error	order	$L^{\infty}$ error	order
7.07E-002	2.1029E-002		2.4996E-002		6.8346E-002
3.51E-002	5.5261E-003	1.9280	6.7907E-003	1.8800	1.7204E-002	1.9900
1.76E-002	1.4303E-003	1.9498	1.8440E-003	1.8806	4.6818E-003	1.8776
8.31E-003	3.6687E-004	1.9630	5.0124E-004	1.8793	1.4688E-003	1.8724

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