多介质流动问题的高精度正保护数值模拟方法

The High-order Accuracy Positivity-preserving Numerical Method for Multi-media Flow Problems

将高精度RKDG(Runge-Kutta Discontinuous Galerkin)正保护格式推广应用于多介质流动问题的数值模拟.通过近似求解双激波Riemann问题来得到界面处流体的流动状态,证明了Riemann问题解的正保护性质,利用RGFM(Real Ghost Fluid Method)界面处理方法定义界面边界条件,将多介质问题转化为单介质问题进行计算,得到一维多介质流动问题的高精度RKDG(Runge-Kutta Discontinuous Galerkin)正保护数值模拟方法.对多个一维问题进行数值模拟,数值结果表明文中所给出的正保护算法,能准确捕捉界面和其他间断的位置.

The positivity preserving high order RKDG （Runge-Kutta Discontinuous Galerkin） method is extended to the simulation of one-dimensional multi-medium flow problem. The fluid states at the interface are obtained by solving the double shock Riemann problem approximate- ly. The positivity preserving property of the solution of the Riemann problem is proved. The in- terface processing method named RGFM （Real Ghost Fluid Method） is used to define the boundary conditions, and the multi-medium problem is transformed into a single media problem to calculate. Therefore, the high-order positivity-preserving numerical method for one dimen- sional multi medium flow problem is obtained. Numerical simulation of a number of one-dimen- sional problems are carried out, and the results show that the proposed algorithm can accurately capture the location of the interface and other discontinuities.