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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