Skip to Main content Skip to Navigation
Journal articles

Construction of a low Mach finite volume scheme for the isentropic Euler system with porosity

Abstract : 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.
Complete list of metadata
Contributor : Jonathan Jung Connect in order to contact the contributor
Submitted on : Tuesday, April 13, 2021 - 4:41:45 PM
Last modification on : Friday, July 8, 2022 - 10:07:40 AM
Long-term archiving on: : Wednesday, July 14, 2021 - 6:51:46 PM


Files produced by the author(s)



Stéphane Dellacherie, Jonathan Jung, Pascal Omnes. Construction of a low Mach finite volume scheme for the isentropic Euler system with porosity. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2021, 55 (3), pp.1199 - 1237. ⟨10.1051/m2an/2021016⟩. ⟨hal-03197310⟩



Record views


Files downloads