An approximate nonlinear projection scheme for a combustion model

¹ MAB UMR 5466 CNRS, Université Bordeaux I, 351 cours de la libération, 33400 Talence, France.
² INRIA Futurs, Domaine de Voluceau-Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France. christophe.berthon@math.u-bordeaux.fr.

Received: 14 May 2002
Revised: 24 February 2003

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.