A RKDG finite element method for the one-dimensional inviscid compressible gas dynamics equations in Lagrangian coordinate

doi:10.1088/1674-1056/22/2/020202

Abstract In this paper, Runge-Kutta Discontinuous Galerkin (RKDG) finite element method is presented to solve the one-dimensional inviscid compressible gas dynamic equations in Lagrangian coordinate. The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method. A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method. For multi-medium fluid simulation, the two cells adjacent to the interface are treated differently from other cells. At first, a linear Riemann solver is applied to calculate the numerical flux at the interface. Numerical examples show that there is some oscillation in the vicinity of the interface. Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical flux at the interface, which suppress the oscillation successfully. Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.

Keywords: compressible gas dynamic equations RKDG finite element method Lagrangian coordinate multi-medium fluid

Received: 04 April 2012
Revised: 06 September 2012
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	02.70.Dh	(Finite-element and Galerkin methods)
	02.60.Lj	(Ordinary and partial differential equations; boundary value problems)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035, 11171038, and 10771019); the Science Reaearch Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZZ12198); and the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2012MS0102).

Corresponding Authors: Zhao Guo-Zhong
E-mail: zhaoguozhongbttc@sina.com

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Zhao Guo-Zhong (赵国忠), Yu Xi-Jun (蔚喜军), Zhang Rong-Pei (张荣培 ) A RKDG finite element method for the one-dimensional inviscid compressible gas dynamics equations in Lagrangian coordinate 2013 Chin. Phys. B 22 020202

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[1]	The discontinuous Petrov-Galerkin method for one-dimensional compressible Euler equations in the Lagrangian coordinate Zhao Guo-Zhong (赵国忠), Yu Xi-Jun (蔚喜军), Guo Peng-Yun (郭鹏云). Chin. Phys. B, 2013, 22(5): 050206.

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A RKDG finite element method for the one-dimensional inviscid compressible gas dynamics equations in Lagrangian coordinate

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