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

Abstract

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

CLC Number:

O241.82

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.

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

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