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.
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