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Semi-Implicit Roe-Type Fluxes for Low-Mach Number Flows

Jean-Frédéric Gerbeau 1 Nathalie Glinsky-Olivier Bernard Larrouturou
1 CAIMAN - Scientific computing, modeling and numerical analysis
CRISAM - Inria Sophia Antipolis - Méditerranée , ENPC - École des Ponts ParisTech, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : Two semi-implicit methods based on the splitting of the Euler equations flux into fluid and acoustic parts applied to low Mach number flows are presented. The first method is based on the splitting of slow and fast eigenvalues of the jacobian matrix of the fluxes and a semi-implicit scheme is constructed by introducing only the fast eigenvalues in the implicit matrices. The second method is based on the splitting of the Euler flux by separating the terms in velocity and the terms in pressure ; this system is solved by a fractional step method. A semi-implicit scheme is obtained by using a linearised implicit scheme for the acoustic step only. These two methods are applied to the convection of a density pulse for Mach numbers equal to 0.1 and 0.01. Accuracy and efficiency of the different schemes are compared.
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https://hal.inria.fr/inria-00073557
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Submitted on : Wednesday, May 24, 2006 - 1:11:16 PM
Last modification on : Thursday, April 5, 2018 - 10:24:16 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:50:18 PM

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  • HAL Id : inria-00073557, version 1

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Jean-Frédéric Gerbeau, Nathalie Glinsky-Olivier, Bernard Larrouturou. Semi-Implicit Roe-Type Fluxes for Low-Mach Number Flows. RR-3132, INRIA. 1997. ⟨inria-00073557⟩

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