Improving the accuracy of discretisations of the vector transport equation on the lowest-order quadrilateral Raviart-Thomas finite elements

Bendall, Thomas M.; Wimmer, Golo Albert

doi:10.1016/j.jcp.2022.111834

Improving the accuracy of discretisations of the vector transport equation on the lowest-order quadrilateral Raviart-Thomas finite elements

Journal Article · Tue Dec 06 00:00:00 EST 2022 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2022.111834· OSTI ID:1903550

^[1]; Wimmer, Golo Albert ^[2]

United Kingdom Meteorological Office, Exeter, Devon (United Kingdom)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Within finite element models of fluids, vector-valued fields such as velocity or momentum variables are commonly discretised using the Raviart-Thomas elements. However, when using the lowest-order quadrilateral Raviart-Thomas elements, standard finite element discretisations of the vector transport equation typically have a low order of spatial accuracy. This paper describes two schemes that improve the accuracy of transporting such vector-valued fields on two-dimensional curved manifolds. The first scheme that is presented reconstructs the transported field in a higher-order function space, where the transport equation is then solved. The second scheme applies a mixed finite element formulation to the vector transport equation, simultaneously solving for the transported field and its vorticity. In this work, an approach to stabilising this mixed vector-vorticity formulation is presented that uses a Streamline Upwind Petrov-Galerkin (SUPG) method. These schemes are then demonstrated, along with their accuracy properties, through some numerical tests. Two new test cases are used to assess the transport of vector-valued fields on curved manifolds, solving the vector transport equation in isolation. The improvement of the schemes is also shown through two standard test cases for rotating shallow-water models.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1903550

Report Number(s):: LA-UR-22-25984

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 474; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Related Subjects

97 MATHEMATICS AND COMPUTING
Mathematics
Recovered finite element method
SUPG
Vector transport
Raviart-Thomas finite elements
Vorticity

Improving the accuracy of discretisations of the vector transport equation on the lowest-order quadrilateral Raviart-Thomas finite elements

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