Energy conserving upwinded compatible finite element schemes for the rotating shallow water equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:401

Article

Wimmer, Golo A.¹  Cotter, Colin J.¹  Bauer, Werner^1,2 

[1] Imperial Coll London, London, England

[2] INRIA Rennes, Rennes, France

关键词: Compatible finite element methods;    Hamiltonian mechanics;    Upwinding;    Shallow water equations;   

DOI  :  10.1016/j.jcp.2019.109016

来源: Elsevier

【 摘 要 】

We present an energy conserving space discretisation of the rotating shallow water equations using compatible finite elements. It is based on an energy and enstrophy conserving Hamiltonian formulation as described in McRae and Cotter (2014), and extends it to include upwinding in the velocity and depth advection to increase stability. Upwinding for velocity in an energy conserving context was introduced for the incompressible Euler equations in Natale and Cotter (2017), while upwinding in the depth field in a Hamiltonian finite element context is newly described here. The energy conserving property is validated by coupling the spatial discretisation to an energy conserving time discretisation. Further, the discretisation is demonstrated to lead to an improved field development with respect to stability when upwinding in the depth field is included. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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