@Article{CiCP-20-188,
author = {Christophe Chalons, Mathieu Girardin and Samuel Kokh},
title = {An All-Regime Lagrange-Projection Like Scheme for the Gas Dynamics Equations on Unstructured Meshes},
journal = {Communications in Computational Physics},
year = {2018},
volume = {20},
number = {1},
pages = {188--233},
abstract = {<p style="text-align: justify;">We propose an all regime Lagrange-Projection like numerical scheme for the
gas dynamics equations. By all regime, we mean that the numerical scheme is able to
compute accurate approximate solutions with an under-resolved discretization with
respect to the Mach number M, i.e. such that the ratio between the Mach number M
and the mesh size or the time step is small with respect to 1. The key idea is to decouple
acoustic and transport phenomenon and then alter the numerical flux in the
acoustic approximation to obtain a uniform truncation error in term of M. This modified
scheme is conservative and endowed with good stability properties with respect
to the positivity of the density and the internal energy. A discrete entropy inequality
under a condition on the modification is obtained thanks to a reinterpretation of the
modified scheme in the Harten Lax and van Leer formalism. A natural extension to
multi-dimensional problems discretized over unstructured mesh is proposed. Then
a simple and efficient semi-implicit scheme is also proposed. The resulting scheme
is stable under a CFL condition driven by the (slow) material waves and not by the
(fast) acoustic waves and so verifies the all regime property. Numerical evidences are
proposed and show the ability of the scheme to deal with tests where the flow regime
may vary from low to high Mach values.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.260614.061115a},
url = {http://global-sci.org/intro/article_detail/cicp/11150.html}
}