Development and Comparison of Numerical Fluxes for LWDG Methods  

作　　者：Jianxian Qiu 

机构地区：[1]Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, China.

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2008年第4期435-459,共25页高等学校计算数学学报（英文版）

基　　金：supported by the European project ADIGMA on the development of innovative solution algorithms for aerodynamic simulations,NSFC grant 10671091,SRF for ROCS,SEM and JSNSF BK2006511.

摘　　要：The discontinuous Galerkin （DO） or local discontinuous Galerkin （LDG） method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. The Lax- Wendroff time discretization procedure is an altemative method for time discretization to the popular total variation diminishing （TVD） Runge-Kutta time discretizations. In this paper, we develop fluxes for the method of DG with Lax-Wendroff time discretization procedure （LWDG） based on different numerical fluxes for finite volume or finite difference schemes, including the first-order monotone fluxes such as the Lax-Friedfichs flux, Godunov flux, the Engquist-Osher flux etc. and the second-order TVD fluxes. We systematically investigate the performance of the LWDG methods based on these different numerical fluxes for convection terms with the objective of obtaining better performance by choosing suitable numerical fluxes. The detailed numerical study is mainly performed for the one-dimensional system case, addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities. Numerical tests are also performed for two dimensional systems.The discontinuous Galerkin (DG) or local discontinuous Galerkin (LDG) method is a spatial discretization procedure for convection-diffusion equations,which employs useful features from high resolution finite volume schemes,such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters.The Lax- Wendroff time discretization procedure is an alternative method for time discretization to the popular total variation diminishing (TVD) Runge-Kutta time discretizations.In this paper,we develop fluxes for the method of DG with Lax-Wendroff time discretiza- tion procedure (LWDG) based on different numerical fluxes for finite volume or finite difference schemes,including the first-order monotone fluxes such as the Lax-Friedrichs flux,Godunov flux,the Engquist-Osher flux etc.and the second-order TVD fluxes.We systematically investigate the performance of the LWDG methods based on these differ- ent numerical fluxes for convection terms with the objective of obtaining better perfor- mance by choosing suitable numerical fluxes.The detailed numerical study is mainly performed for the one-dimensional system case,addressing the issues of CPU cost,ac- curacy,non-oscillatory property,and resolution of discontinuities.Numerical tests are also performed for two dimensional systems.

关 键 词：Discontinuous Galerkin method Lax-Wendroff type time discretization numerical flux approximate Riemann solver timiter WENO scheme high order accuracy. 

分 类 号：O24[理学—计算数学]