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.
@article{M2AN_2003__37_3_451_0,
author = {Berthon, Christophe and Reignier, Didier},
title = {An approximate nonlinear projection scheme for a combustion model},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {37},
year = {2003},
pages = {451-478},
doi = {10.1051/m2an:2003037},
mrnumber = {1994312},
zbl = {1062.65102},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2003__37_3_451_0}
}
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) pp. 451-478. doi : 10.1051/m2an:2003037. http://gdmltest.u-ga.fr/item/M2AN_2003__37_3_451_0/
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