The discontinuous Galerkin method with Lax–Wendroff type time discretizations

• DOI: 10.1016/j.cma.2004.11.007
• Publication Date: 2005-01-13T13:49:19Z
• Authors: Jianxian Qiu; Michael Dumbser; Chi-Wang Shu
• Keywords: WENO scheme; Runge-Kutta method; discontinuous Galerkin method; high order accuracy; 0101 mathematics; 01 natural sciences; Lax-Wendroff type time discretization; limiter

Abstract In this paper we develop a Lax–Wendroff time discretization procedure for the discontinuous Galerkin method (LWDG) to solve hyperbolic conservation laws. This is an alternative method for time discretization to the popular total variation diminishing (TVD) Runge–Kutta time discretizations. The LWDG is a one step, explicit, high order finite element method. The limiter is performed once every time step. As a result, LWDG is more compact than Runge–Kutta discontinuous Galerkin (RKDG) and the Lax–Wendroff time discretization procedure is more cost effective than the Runge–Kutta time discretizations for certain problems including two-dimensional Euler systems of compressible gas dynamics when nonlinear limiters are applied.