中国物理B ›› 2013, Vol. 22 ›› Issue (2): 20202-020202.doi: 10.1088/1674-1056/22/2/020202

• GENERAL • 上一篇    下一篇

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

赵国忠a, 蔚喜军b, 张荣培c   

  1. a Faculty of Mathematics, Baotou Teachers' College, Baotou 014030, China;
    b Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
    c School of Science, Liaoning Shihua University, Fushun 113001, China
  • 收稿日期:2012-04-04 修回日期:2012-09-06 出版日期:2013-01-01 发布日期:2013-01-01
  • 基金资助:
    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).

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

Zhao Guo-Zhong (赵国忠)a, Yu Xi-Jun (蔚喜军)b, Zhang Rong-Pei (张荣培 )c   

  1. a Faculty of Mathematics, Baotou Teachers' College, Baotou 014030, China;
    b Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
    c School of Science, Liaoning Shihua University, Fushun 113001, China
  • Received:2012-04-04 Revised:2012-09-06 Online:2013-01-01 Published:2013-01-01
  • Contact: Zhao Guo-Zhong E-mail:zhaoguozhongbttc@sina.com
  • Supported by:
    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).

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摘要： 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.

关键词: compressible gas dynamic equations, RKDG finite element method, Lagrangian coordinate, multi-medium fluid

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.

Key words: compressible gas dynamic equations, RKDG finite element method, Lagrangian coordinate, multi-medium fluid

中图分类号:  (Partial differential equations)

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