Year: 2020
Author: Andrea Thomann, Markus Zenk, Gabriella Puppo, Christian Klingenberg
Communications in Computational Physics, Vol. 28 (2020), Iss. 2 : pp. 591–620
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2019-0123
Communications in Computational Physics, Vol. 28 (2020), Iss. 2 : pp. 591–620
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Finite volume methods Euler equations positivity preserving asymptotic preserving relaxation low Mach scheme IMEX schemes.