A finite element exterior calculus framework for the rotating shallow-water equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:257

Article

Cotter, C. J.¹  Thuburn, J.² 

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW18 4RP, England

[2] Univ Exeter, Coll Engn Math & Phys Sci, Exeter EX4 4QF, Devon, England

关键词: Finite element exterior calculus;    Potential vorticity;    Numerical weather prediction;    Shallow-water equations;   

DOI  :  10.1016/j.jcp.2013.10.008

来源: Elsevier

【 摘 要 】

We describe discretisations of the shallow-water equations on the sphere using the framework of finite element exterior calculus, which are extensions of the mimetic finite difference framework presented in Ringler (2010) [11]. The exterior calculus notation provides a guide to which finite element spaces should be used for which physical variables, and unifies a number of desirable properties. We present two formulations: a primal formulation in which the finite element spaces are defined on a single mesh, and a primal-dual formulation in which finite element spaces on a dual mesh are also used. Both formulations have velocity and layer depth as prognostic variables, but the exterior calculus framework leads to a conserved diagnostic potential vorticity. In both formulations we show how to construct discretisations that have mass-consistent (constant potential vorticity stays constant), stable and oscillation-free potential vorticity advection. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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