A unified approach to energy conservation and potential vorticity dynamics for arbitrarily-structured C-grids

JOURNAL OF COMPUTATIONAL PHYSICS

卷:229

Article

Ringler, T. D.¹  Thuburn, J.²  Klemp, J. B.³  Skamarock, W. C.³ 

[1] Los Alamos Natl Lab, Div Theoret, Los Alamos, NM 87545 USA

[2] Univ Exeter, Math Res Inst, Sch Engn Comp & Math, Exeter EX4 4QF, Devon, England

[3] Natl Ctr Atmospher Res, Boulder, CO 80307 USA

关键词: C-grid;    Voronoi diagram;    Potential vorticity;    Shallow-water equations;   

DOI  :  10.1016/j.jcp.2009.12.007

来源: Elsevier

【 摘 要 】

A numerical scheme applicable to arbitrarily-structured C-grids is presented for the nonlinear shallow-water equations. By discretizing the vector-invariant form of the momentum equation, the relationship between the nonlinear Coriolis force and the potential vorticity flux can be used to guarantee that mass, velocity and potential vorticity evolve in a consistent and compatible manner. Underpinning the consistency and compatibility of the discrete system is the construction of an auxiliary thickness equation that is staggered from the primary thickness equation and collocated with the vorticity field. The numerical scheme also exhibits conservation of total energy to within time-truncation error. Simulations of the standard shallow-water test cases confirm the analysis and show convergence rates between 1st- and 2nd-order accuracy when discretizing the system with quasi-uniform spherical Voronoi diagrams. The numerical method is applicable to a wide class of meshes, including latitude-longitude grids, Voronoi diagrams, Delaunay triangulations and conformally-mapped cubed-sphere meshes. Published by Elsevier Inc.

【 授权许可】

Free