TY - JOUR
T1 - An All Speed Second Order IMEX Relaxation Scheme for the Euler Equations
AU - Thomann , Andrea
AU - Zenk , Markus
AU - Puppo , Gabriella
AU - Klingenberg , Christian
JO - Communications in Computational Physics
VL - 2
SP - 591
EP - 620
PY - 2020
DA - 2020/06
SN - 28
DO - http://doi.org/10.4208/cicp.OA-2019-0123
UR - https://global-sci.org/intro/article_detail/cicp/16942.html
KW - Finite volume methods, Euler equations, positivity preserving, asymptotic preserving, relaxation, low Mach scheme, IMEX schemes.
AB - <p style="text-align: justify;">We present an implicit-explicit finite volume scheme for the Euler equations.
We start from the non-dimensionalised Euler equations where we split the pressure in
a slow and a fast acoustic part. We use a Suliciu type relaxation model which we split
in an explicit part, solved using a Godunov-type scheme based on an approximate
Riemann solver, and an implicit part where we solve an elliptic equation for the fast
pressure. The relaxation source terms are treated projecting the solution on the equilibrium manifold. The proposed scheme is positivity preserving with respect to the
density and internal energy and asymptotic preserving towards the incompressible
Euler equations. For this first order scheme we give a second order extension which
maintains the positivity property. We perform numerical experiments in 1D and 2D to
show the applicability of the proposed splitting and give convergence results for the
second order extension.</p>