Lax-Wendroff Discontinuous Galerkin Method For Multi-Medium Flow

certain time. Discontinuous Galerkin (DG) finite element method provides a good way to handle the discontinuity. The numerical solution is allowed to be discontinuous on the cell boundary, which enhances the resolution across the discontinuity. When an appropriate limiter is applied, the convergence and stability of the scheme is ensured.In this paper, we explore the Lax-Wendroff (LW) type time discretization as an alternative procedure to the Runge-Kutta time discretization adopted for the computa-tion of multi-medium flow using MGFM. The Lax-Wendroff type time discretization is based on a Taylor expansion in time, utilizing the partial differential equations repeat-edly to convert all time derivatives to spatial derivatives, and then to discretize new flux constructed by these derivatives using DG method. Compared with the Runge-Kutta time discretization, an advantage of the LW time discretization is the apparent saving in computational cost and memory requirement, since the substeps in time are no longer required when advancing the scheme to a new time level.