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.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2021009
Keywords: Central-upwind schemes, numerical dissipation, local speeds of propagation, Euler equations of gas dynamics, thermal rotating shallow water equations
@article{M2AN_2021__55_3_713_0,
author = {Kurganov, Alexander and Liu, Yongle and Zeitlin, Vladimir},
title = {Numerical dissipation switch for two-dimensional central-upwind schemes},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {713--734},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {3},
doi = {10.1051/m2an/2021009},
mrnumber = {4253170},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021009/}
}
TY - JOUR AU - Kurganov, Alexander AU - Liu, Yongle AU - Zeitlin, Vladimir TI - Numerical dissipation switch for two-dimensional central-upwind schemes JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 713 EP - 734 VL - 55 IS - 3 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021009/ DO - 10.1051/m2an/2021009 LA - en ID - M2AN_2021__55_3_713_0 ER -
%0 Journal Article %A Kurganov, Alexander %A Liu, Yongle %A Zeitlin, Vladimir %T Numerical dissipation switch for two-dimensional central-upwind schemes %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 713-734 %V 55 %N 3 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021009/ %R 10.1051/m2an/2021009 %G en %F M2AN_2021__55_3_713_0
Kurganov, Alexander; Liu, Yongle; Zeitlin, Vladimir. Numerical dissipation switch for two-dimensional central-upwind schemes. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 3, pp. 713-734. doi: 10.1051/m2an/2021009
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