Classical finite volume schemes for the Euler system are not accurate at low Mach number and some fixes have to be used and were developed in a vast literature over the last two decades. The question we are interested in in this article is: What about if the porosity is no longer uniform? We first show that this problem may be understood on the linear wave equation taking into account porosity. We explain the influence of the cell geometry on the accuracy property at low Mach number. In the triangular case, the stationary space of the Godunov scheme approaches well enough the continuous space of constant pressure and divergence-free velocity, while this is not the case in the Cartesian case. On Cartesian meshes, a fix is proposed and accuracy at low Mach number is proved to be recovered. Based on the linear study, a numerical scheme and a low Mach fix for the non-linear system, with a non-conservative source term due to the porosity variations, is proposed and tested.
Keywords: low Mach limit, finite volume schemes, porosity, Euler equations, numerical diffusion
@article{M2AN_2021__55_3_1199_0,
author = {Dellacherie, St\'ephane and Jung, Jonathan and Omnes, Pascal},
title = {Construction of a low {Mach} finite volume scheme for the isentropic {Euler} system with porosity},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1199--1237},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {3},
doi = {10.1051/m2an/2021016},
mrnumber = {4269467},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021016/}
}
TY - JOUR AU - Dellacherie, Stéphane AU - Jung, Jonathan AU - Omnes, Pascal TI - Construction of a low Mach finite volume scheme for the isentropic Euler system with porosity JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 1199 EP - 1237 VL - 55 IS - 3 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021016/ DO - 10.1051/m2an/2021016 LA - en ID - M2AN_2021__55_3_1199_0 ER -
%0 Journal Article %A Dellacherie, Stéphane %A Jung, Jonathan %A Omnes, Pascal %T Construction of a low Mach finite volume scheme for the isentropic Euler system with porosity %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 1199-1237 %V 55 %N 3 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021016/ %R 10.1051/m2an/2021016 %G en %F M2AN_2021__55_3_1199_0
Dellacherie, Stéphane; Jung, Jonathan; Omnes, Pascal. Construction of a low Mach finite volume scheme for the isentropic Euler system with porosity. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 3, pp. 1199-1237. doi: 10.1051/m2an/2021016
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