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首页> 外文期刊>Journal of Scientific Computing >A Numerical Comparison Of The Lax-wendroff Discontinuous Galerkin Method Based On Different Numerical Fluxes
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A Numerical Comparison Of The Lax-wendroff Discontinuous Galerkin Method Based On Different Numerical Fluxes

机译：不同数值通量的Lax-wendroff不连续Galerkin方法的数值比较

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摘要

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 lim-iters. 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.
机译：间断Galerkin（DG）方法是一种空间离散过程，它采用了高分辨率有限体积方案的有用功能，例如用作数值通量和限制剂的精确或近似Riemann求解器。在[（2005）。计算方法应用。机甲。 194，4528]，我们为DG方法（LWDG）开发了Lax-Wendroff时间离散化程序，这是流行的总变化量减小（TVD）Runge-Kutta时间离散化的时间离散化方法。在文献中的大多数DG论文中，由于其简单性，使用了Lax-Friedrichs数值通量，尽管也可以使用许多其他数值通量。在本文中，我们基于不同的数值通量，包括Godunov通量，Engquist-Osher通量等一阶单调通量，二阶TVD通量和广义Riemann，系统地研究了LWDG方法的性能。解算器，其目的是通过选择合适的数值通量来获得更好的性能。详细的数值研究主要针对一维系统情况进行，以解决CPU成本，准确性，非振荡特性和不连续性的解决问题。还对二维系统执行了数值测试。

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