NDLI: A Numerical Comparison of the Lax–Wendroff Discontinuous Galerkin Method Based on Different Numerical Fluxes

Content Provider	Springer Nature Link
Author	Qiu, Jianxian
Copyright Year	2006
Abstract	Discontinuous Galerkin (DG) method is a spatial discretization procedure, employing useful features from high-resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. In [(2005). Comput. Methods Appl. Mech. Eng. 194, 4528], we developed a Lax–Wendroff time discretization procedure for the DG method (LWDG), an alternative method for time discretization to the popular total variation diminishing (TVD) Runge–Kutta time discretizations. In most of the DG papers in the literature, the Lax–Friedrichs numerical flux is used due to its simplicity, although there are many other numerical fluxes, which could also be used. In this paper, we systematically investigate the performance of the LWDG method based on different numerical fluxes, including the first-order monotone fluxes such as the Godunov flux, the Engquist–Osher flux, etc., the second-order TVD fluxes and generalized Riemann solver, 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.
Starting Page	345
Ending Page	367
Page Count	23
File Format	PDF
ISSN	08857474
Journal	Journal of Scientific Computing
Volume Number	30
Issue Number	3
e-ISSN	15737691
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2006-09-19
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Discontinuous Galerkin method Lax–Wendroff type time discretization numerical flux approximate Riemann solver limiter WENO scheme high-order accuracy Mathematical and Computational Physics ApplicationMathematics/Computational Methods of Engineering Computational Mathematics and Numerical Analysis Algorithms
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Engineering Computational Theory and Mathematics Computational Mathematics Numerical Analysis Software

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