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An approximate nonlinear projection scheme for a combustion model

Published online by Cambridge University Press:  15 April 2004

Christophe Berthon  and
Didier Reignier
Christophe Berthon
Affiliation:
MAB UMR 5466 CNRS, Université Bordeaux I, 351 cours de la libération, 33400 Talence, France. INRIA Futurs, Domaine de Voluceau-Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France. christophe.berthon@math.u-bordeaux.fr.
Didier Reignier
Affiliation:
MAB UMR 5466 CNRS, Université Bordeaux I, 351 cours de la libération, 33400 Talence, France.
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Abstract

The paper deals with the numerical resolution of the convection-diffusion system which arises when modeling combustion for turbulent flow. The considered model is of compressible turbulent reacting type where the turbulence-chemistry interactions are governed by additional balance equations. The system of PDE's, that governs such a model, turns out to be in non-conservation form and usual numerical approaches grossly fail in the capture of viscous shock layers. Put in other words, classical finite volume methods induce large errors when approximated the convection-diffusion extracted system. To solve this difficulty, recent works propose a nonlinear projection scheme based on cancellation phenomenon of relevant dissipation rates of entropy. Unfortunately, such a property never holds in the present framework. The nonlinear projection procedures are thus extended.

Keywords

Hyperbolic systems in nonconservation formfinite volume methodsnonlinear projection method.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 3 , May 2003 , pp. 451 - 478
Copyright
© EDP Sciences, SMAI, 2003

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