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

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Title: Energy conserving upwinded compatible finite element schemes for the rotating shallow water equations
Authors: Wimmer, GA
Cotter, CJ
Bauer, W
Item Type: Journal Article
Abstract: 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.
Issue Date: 15-Jan-2020
Date of Acceptance: 5-Oct-2019
URI: http://hdl.handle.net/10044/1/92425
DOI: 10.1016/j.jcp.2019.109016
ISSN: 0021-9991
Publisher: Elsevier
Start Page: 1
End Page: 18
Journal / Book Title: Journal of Computational Physics
Volume: 401
Copyright Statement: © 2019 Elsevier Inc. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor/Funder: Natural Environment Research Council (NERC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: NE/M013634/1
EP/R029423/1
Keywords: Science & Technology
Technology
Physical Sciences
Computer Science, Interdisciplinary Applications
Physics, Mathematical
Computer Science
Physics
Compatible finite element methods
Hamiltonian mechanics
Upwinding
Shallow water equations
Science & Technology
Technology
Physical Sciences
Computer Science, Interdisciplinary Applications
Physics, Mathematical
Computer Science
Physics
Compatible finite element methods
Hamiltonian mechanics
Upwinding
Shallow water equations
math.NA
math.NA
Applied Mathematics
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status: Published
Article Number: ARTN 109016
Online Publication Date: 2019-10-11
Appears in Collections:Applied Mathematics and Mathematical Physics
Mathematics



This item is licensed under a Creative Commons License Creative Commons