统一坐标系下二维气动方程组的Runge-Kutta间断Galerkin有限元方法

Runge-Kutta discontinuous Galerkin finite element method for two-dimensional gas dynamic equations in unified coordinate

构造了统一坐标系下二维可压缩气动方程组的Runge-Kutta间断Galerkin(RKDG)有限元格式.文中将流体力学方程组和几何守恒律统一求解,所有计算都在固定的网格上进行,在计算过程中不需要网格节点的速度信息.文中对几个数值算例进行了数值模拟,得到了较好的数值模拟结果.

In this paper we develop the Runge-Kutta discontinuous Galerkin finite element method for two-dimensional compressible gas dynamic equations in unified coordinate.The equations for fluid dynamics and geometry conservation laws are solved simultaneously. All the calculations can be performed on the fixed meshes.The information about the grid velocities is not needed in calculation.Some numerical examples are given to evaluate the efficiency and the reliability of the scheme.The numerical results show that the algorithm works well.