An approximate nonlinear projection scheme for a combustion model
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 37 (2003) no. 3, pp. 451-478.

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.

DOI : https://doi.org/10.1051/m2an:2003037
Classification : 65M99,  76L05,  76M25
Mots clés : hyperbolic systems in nonconservation form, finite volume methods, nonlinear projection method
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author = {Berthon, Christophe and Reignier, Didier},
title = {An approximate nonlinear projection scheme for a combustion model},
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Berthon, Christophe; Reignier, Didier. An approximate nonlinear projection scheme for a combustion model. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 37 (2003) no. 3, pp. 451-478. doi : 10.1051/m2an:2003037. http://www.numdam.org/articles/10.1051/m2an:2003037/

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