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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.
Mots-clés : hyperbolic systems in nonconservation form, finite volume methods, nonlinear projection method
@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 },
pages = {451--478},
publisher = {EDP-Sciences},
volume = {37},
number = {3},
year = {2003},
doi = {10.1051/m2an:2003037},
zbl = {1062.65102},
mrnumber = {1994312},
language = {en},
url = {https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003037/}
}
TY - JOUR AU - Berthon, Christophe AU - Reignier, Didier TI - An approximate nonlinear projection scheme for a combustion model JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2003 SP - 451 EP - 478 VL - 37 IS - 3 PB - EDP-Sciences UR - https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003037/ DO - 10.1051/m2an:2003037 LA - en ID - M2AN_2003__37_3_451_0 ER -
%0 Journal Article %A Berthon, Christophe %A Reignier, Didier %T An approximate nonlinear projection scheme for a combustion model %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2003 %P 451-478 %V 37 %N 3 %I EDP-Sciences %U https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003037/ %R 10.1051/m2an:2003037 %G en %F 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 , Tome 37 (2003) no. 3, pp. 451-478. doi : 10.1051/m2an:2003037. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003037/
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