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

作者：Zhao Guo Zhong^*; Yu Xi Jun; Zhang Rong Pei

来源：Chinese Physics B, 2013, 22(2): 020202.

DOI：10.1088/1674-1056/22/2/020202

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

In this paper, Runge-Kutta Discontinuous Galerkin (RKDG) finite element method is presented to solve the one-dimensional 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 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 suppresses the oscillation successfully. Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.

• 出版日期2013-2
• 单位辽宁石油化工大学; 北京应用物理与计算数学研究所; 内蒙古科技大学包头师范学院