Impact and importance of hyperdiffusion on the spectral element method: A linear dispersion analysis

JOURNAL OF COMPUTATIONAL PHYSICS

卷:375

Article

Ullrich, Paul A.¹  Reynolds, Daniel R.²  Guerra, Jorge E.¹  Taylor, Mark A.³ 

[1] Univ Calif Davis, Dept Land Air & Water Resources, Davis, CA 95616 USA

[2] Southern Methodist Univ, Dept Math, POB 750156, Dallas, TX 75257 USA

[3] Sandia Natl Labs, POB 5800,MS 1320, Albuquerque, NM 87185 USA

关键词: High-order;    Dispersion analysis;    Spectral-element method;    Finite-element methods;    Linear gravity waves;    Dynamical core;   

DOI  :  10.1016/j.jcp.2018.06.035

来源: Elsevier

【 摘 要 】

The spectral element method (SEM) is a mimetic finite element method with several properties that make it a desirable choice for numerical modeling. Although the linear dispersion properties of this method have been analyzed extensively for the case of the 1D inviscid advection equation, practical implementations of the SEM frequently employ hyperdiffusion for stabilization. As argued in this paper, hyperdiffusion has a pronounced impact on the accuracy of the discrete wave modes and the dispersive properties of the SEM. When applied with an appropriately large coefficient, hyperdiffusion is effective at removing the spectral gap and improving the stability of the 1D advection equation. This study also considers the SEM as applied to the 2D linearized shallow-water equations, where hyperdiffusion in the form of scalar diffusion, divergence damping, and vorticity damping are analyzed. To the extent possible, guidance on the choice of hyperdiffusion coefficients is provided. A brief discussion of the comparative impact of local element filtering is included. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free