@Article{CiCP-10-1,
author = {},
title = {All Speed Scheme for the Low Mach Number Limit of the Isentropic Euler Equations},
journal = {Communications in Computational Physics},
year = {2011},
volume = {10},
number = {1},
pages = {1--31},
abstract = {<p style="text-align: justify;">An all speed scheme for the Isentropic Euler equations is presented in this
paper. When the Mach number tends to zero, the compressible Euler equations converge
to their incompressible counterpart, in which the density becomes a constant. Increasing
approximation errors and severe stability constraints are the main difficulty
in the low Mach regime. The key idea of our all speed scheme is the special semi-implicit
time discretization, in which the low Mach number stiff term is divided into
two parts, one being treated explicitly and the other one implicitly. Moreover, the flux
of the density equation is also treated implicitly and an elliptic type equation is derived
to obtain the density. In this way, the correct limit can be captured without requesting
the mesh size and time step to be smaller than the Mach number. Compared with
previous semi-implicit methods [11,13,29], firstly, nonphysical oscillations can be suppressed
by choosing proper parameter, besides, only a linear elliptic equation needs to
be solved implicitly which reduces much computational cost. We develop this semi-implicit
time discretization in the framework of a first order Local Lax-Friedrichs (or
Rusanov) scheme and numerical tests are displayed to demonstrate its performances.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.210709.210610a},
url = {https://global-sci.com/article/80912/all-speed-scheme-for-the-low-mach-number-limit-of-the-isentropic-euler-equations}
}