The 'recovered space' advection scheme for lowest-order compatible finite element methods
OA Location
Author(s)
Bendall, Thomas M
Cotter, Colin J
Shipton, Jemma
Type
Journal Article
Abstract
We present a new compatible finite element advection scheme for the compressible Euler equations. Unlike the discretisations described in Cotter and Kuzmin (2016) and Shipton et al. (2018), the discretisation uses the lowest-order family of compatible finite element spaces, but still retains second-order numerical accuracy. This scheme obtains this second-order accuracy by first ‘recovering’ the function in higher-order spaces, before using the discontinuous Galerkin advection schemes of Cotter and Kuzmin (2016). As well as describing the scheme, we also present its stability properties and a strategy for ensuring boundedness. We then demonstrate its properties through some numerical tests, before presenting its use within a model solving the compressible Euler equations.
Date Issued
2019-08-01
Date Acceptance
2019-04-05
Citation
Journal of Computational Physics, 2019, 390, pp.342-358
ISSN
0021-9991
Publisher
Elsevier
Start Page
342
End Page
358
Journal / Book Title
Journal of Computational Physics
Volume
390
Copyright Statement
© 2019 Elsevier Inc. All rights reserved.
Sponsor
Natural Environment Research Council (NERC)
Natural Environment Research Council (NERC)
Engineering & Physical Science Research Council (EPSRC)
Natural Environment Research Council (NERC)
Engineering & Physical Science Research Council (EPSRC)
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000468887700018&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
NE/I02013X/1
NE/K006789/1
EP/L000407/1
NE/M013634/1
EP/R029423/1
Subjects
Science & Technology
Technology
Physical Sciences
Computer Science, Interdisciplinary Applications
Physics, Mathematical
Computer Science
Physics
Advection scheme
Discontinuous Galerkin
Compatible finite element methods
Numerical weather prediction
SHALLOW-WATER EQUATIONS
APPROXIMATIONS
Publication Status
Published
Date Publish Online
2019-04-12