Volume 55, Number 3, May-June 2021
|Page(s)||713 - 734|
|Published online||05 May 2021|
Numerical dissipation switch for two-dimensional central-upwind schemes
Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, P.R. China
2 SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen 518055, P.R. China
3 Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P.R. China
4 Laboratoire de Météorologie Dynamique, Sorbonne Université (SU), Ecole Normale Supérieure (ENS), CNRS, Paris 75231, France
* Corresponding author: firstname.lastname@example.org
Accepted: 17 February 2021
We propose a numerical dissipation switch, which helps to control the amount of numerical dissipation present in central-upwind schemes. Our main goal is to reduce the numerical dissipation without risking oscillations. This goal is achieved with the help of a more accurate estimate of the local propagation speeds in the parts of the computational domain, which are near contact discontinuities and shears. To this end, we introduce a switch parameter, which depends on the distributions of energy in the x- and y-directions. The resulting new central-upwind is tested on a number of numerical examples, which demonstrate the superiority of the proposed method over the original central-upwind scheme.
Mathematics Subject Classification: 76M12 / 65M08 / 35L65 / 86-08
Key words: Central-upwind schemes / numerical dissipation / local speeds of propagation / Euler equations of gas dynamics / thermal rotating shallow water equations
© EDP Sciences, SMAI 2021
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