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Dispersion-dissipation analysis of triangular numerical-flux-based discontinuous Galerkin method for elastic wave equations
Journal of Computational Physics ( IF 3.8 ) Pub Date : 2020-06-08 , DOI: 10.1016/j.jcp.2020.109630
Xijun He , Dinghui Yang , Chujun Qiu

This paper presents a quantitative dispersion-dissipation and stability analysis of the triangle-based discontinuous Galerkin method (DGM) for simulating elastic wave propagation. The analysis is carried out for both P- and S-waves, with semi-discrete and fully discrete cases. The DGM is based on the 1st-order hyperbolic system with numerical flux formulations. The semi-discrete analysis is considered with respect to different numerical fluxes, different mesh configurations, and various ratios of P-wave velocity (Vp) and S-wave velocity (Vs). The LLF numerical flux and Godunov numerical flux are employed for the analysis. We consider two triangular mesh configurations, which are compared with the quadrilateral mesh. A fully discrete analysis is also presented where 3rd-order total variation diminishing Runge-Kutta temporal discretization is used. The results demonstrate that the numerical dispersion and dissipation vary significantly with the mesh configurations, but they show small difference with respect to the Vp /Vs values. In addition, the performance of LLF flux is similar to that of Godunov flux.



中文翻译:

基于三角数值通量的不连续Galerkin方法求解弹性波方程的色散

本文介绍了基于三角形的不连续伽勒金方法(DGM)来模拟弹性波传播的定量色散耗散和稳定性分析。对于半离散和完全离散的情况,都对P波S波进行了分析。DGM基于带有数值通量公式的一阶双曲系统。对于不同的数值通量,不同的网格配置以及各种P波速比(Vp)和S波速度(Vs)。分析采用LLF数值通量和Godunov数值通量。我们考虑两个三角形网格配置,将它们与四边形网格进行比较。还提出了使用三阶总方差减小Runge-Kutta时间离散化的完全离散分析。结果表明,数值色散和耗散随网格配置的不同而有很大差异,但相对于网格,它们显示出很小的差异。Vp /Vs价值观。此外,LLF通量的性能类似于Godunov通量。

更新日期:2020-06-08
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