The discontinuous Galerkin method with Lax-Wendroff type time discretizations
The discontinuous Galerkin method with Lax-Wendroff type time discretizations
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DOI：
10.1016/j.cma.2004.11.007
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发表时间：
2005-10
影响因子：
7.2
通讯作者：
J. Qiu;M. Dumbser;Chi-Wang Shu
中科院分区：
文献类型：
--
作者：
J. Qiu;M. Dumbser;Chi-Wang Shu
本文发展了求解双曲型守恒律方程的间断Galerkin方法的Lax-Wendroff时间离散方法。这是一个替代方法的时间离散流行的总变差递减（TVD）龙格库塔时间离散。LWDG是一种一步显式高阶有限元方法。每个时间步执行一次限制器。因此，LWDG比Runge-Kutta间断Galerkin（RKDG）更紧凑，Lax-Wendroff时间离散过程比Runge-Kutta时间离散更经济有效，适用于某些问题，包括二维可压缩气体动力学Euler系统，当应用非线性限制器时。
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.