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

Classification:  65M99,  76L05,  76M25
Keywords: hyperbolic systems in nonconservation form, finite volume methods, nonlinear projection method
     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},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {3},
     year = {2003},
     pages = {451-478},
     doi = {10.1051/m2an:2003037},
     zbl = {1062.65102},
     mrnumber = {1994312},
     language = {en},
     url = {}
An approximate nonlinear projection scheme for a combustion model. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 3, pp. 451-478. doi : 10.1051/m2an:2003037.

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