Higher-order compatible finite element schemes for the nonlinear rotating shallow water equations on the sphere

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Title: Higher-order compatible finite element schemes for the nonlinear rotating shallow water equations on the sphere
Authors: Shipton, J
Gibson, TH
Cotter, CJ
Item Type: Journal Article
Abstract: We describe a compatible finite element discretisation for the shallow water equations on the rotating sphere, concentrating on integrating consistent upwind stabilisation into the framework. Although the prognostic variables are velocity and layer depth, the discretisation has a diagnostic potential vorticity that satisfies a stable upwinded advection equation through a Taylor-Galerkin scheme; this provides a mechanism for dissipating enstrophy at the gridscale whilst retaining optimal order consistency. We also use upwind discontinuous Galerkin schemes for the transport of layer depth. These transport schemes are incorporated into a semi-implicit formulation that is facilitated by a hybridisation method for solving the resulting mixed Helmholtz equation. We illustrate our discretisation with some standard rotating sphere test problems.
Issue Date: 15-Dec-2018
Date of Acceptance: 17-Aug-2018
ISSN: 0021-9991
Publisher: Elsevier
Start Page: 1121
End Page: 1137
Journal / Book Title: Journal of Computational Physics
Volume: 375
Copyright Statement: © 2018 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (
Sponsor/Funder: Natural Environment Research Council (NERC)
Engineering & Physical Science Research Council (EPSRC)
Natural Environment Research Council (NERC)
Natural Environment Research Council (NERC)
Funder's Grant Number: NE/K006789/1
Keywords: math.NA
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Applied Mathematics
Publication Status: Published
Online Publication Date: 2018-09-17
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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