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

作　　者：赵国忠 蔚喜军 张荣培 

机构地区：[1]Faculty of Mathematics,Baotou Teachers'College [2]Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics [3]School of Science,Liaoning Shihua University

出　　处：《Chinese Physics B》2013年第2期50-63,共14页中国物理B（英文版）

基　　金：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);the Natural Science Foundation of Inner Mongolia Autonomous Region,China (Grant No. 2012MS0102)

摘　　要：In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a 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 ？ux 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 ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a 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 ？ux 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 ？ux at the interface,which suppresses 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 

分 类 号：O354[理学—流体力学] TV133[理学—力学]