Energy-enstrophy conserving compatible finite element schemes for the
rotating shallow water equations with slip boundary conditions
rotating shallow water equations with slip boundary conditions
File(s)
Published version
Author(s)
Bauer, Werner
Cotter, Colin J
Type
Journal Article
Abstract
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.
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.
Date Issued
2018-11-15
Date Acceptance
2018-06-27
Citation
Journal of Computational Physics, 2018, 373, pp.171-187
ISSN
0021-9991
Publisher
Elsevier
Start Page
171
End Page
187
Journal / Book Title
Journal of Computational Physics
Volume
373
Copyright Statement
© 2018 The Authors. Published by Elsevier Inc. This
is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
Sponsor
Commission of the European Communities
Identifier
http://arxiv.org/abs/1801.00691v3
Grant Number
657016
Subjects
math.NA
math.NA
physics.ao-ph
Notes
Revision in response to reviewers at JCP
Publication Status
Published
Date Publish Online
2018-06-30