Numerical dissipation switch for two-dimensional central-upwind schemes

¹ 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: liuyl2017@mail.sustech.edu.cn

Received: 1 June 2020
Accepted: 17 February 2021

Abstract

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.