Energy-enstrophy conserving compatible finite element schemes for the rotating shallow water equations with slip boundary conditions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:373

Article

关键词: Structure preserving discretisation;    Compatible finite element methods;    Geophysical fluid dynamics;    Potential vorticity;   

DOI  :  10.1016/j.jcp.2018.06.071

来源: Elsevier

【 摘 要 】

We describe an energy-enstrophy conserving discretisation for the rotating shallow water equations with slip boundary conditions. This relaxes the assumption of boundary-free domains (periodic solutions or the surface of a sphere, for example) in the energy-enstrophy conserving formulation of McRae and Cotter (2014). This discretisation requires extra prognostic vorticity variables on the boundary in addition to the prognostic velocity and layer depth variables. The energy-enstrophy conservation properties hold for any appropriate set of compatible finite element spaces defined on arbitrary meshes with arbitrary boundaries. We demonstrate the conservation properties of the scheme with numerical solutions on a rotating hemisphere. (C) 2018 The Authors. Published by Elsevier Inc.

【 授权许可】

Free