Elementary dispersion analysis of some mimetic discretizations on triangular C-grids

JOURNAL OF COMPUTATIONAL PHYSICS

卷:330

Article

Korn, P.¹  Danilov, S.^2,3 

[1] Max Planck Inst Meteorol, Hamburg, Germany

[2] Alfred Wegener Inst Polar & Marine Res, Bremerhaven, Germany

[3] AM Obukhov Inst Atmospher Phys, Moscow, Russia

关键词: C-grid;    Dispersion analysis;    Mimetic discretization;    Wave propagation;    Spurious modes;    Triangular grid;   

DOI  :  10.1016/j.jcp.2016.10.059

来源: Elsevier

【 摘 要 】

Spurious modes supported by triangular C-grids limit their application for modeling large-scale atmospheric and oceanic flows. Their behavior can be modified within a mimetic approach that generalizes the scalar product underlying the triangular C-grid discretization. The mimetic approach provides a discrete continuity equation which operates on an averaged combination of normal edge velocities instead of normal edge velocities proper. An elementary analysis of the wave dispersion of the new discretization for Poincare, Rossby and Kelvin waves shows that, although spurious Poincare modes are preserved, their frequency tends to zero in the limit of small wavenumbers, which removes the divergence noise in this limit. However, the frequencies of spurious and physical modes become close on shorter scales indicating that spurious modes can be excited unless high frequency short-scale motions are effectively filtered in numerical codes. We argue that filtering by viscous dissipation is more efficient in the mimetic approach than in the standard C-grid discretization. Lumping of mass matrices appearing with the velocity time derivative in the mimetic discretization only slightly reduces the accuracy of the wave dispersion and can be used in practice. Thus, the mimetic approach cures some difficulties of the traditional triangular C-grid discretization but may still need appropriately tuned viscosity to filter small scales and high frequencies in solutions of full primitive equations when these are excited by nonlinear dynamics. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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