# An approximate nonlinear projection scheme for a combustion model

Christophe Berthon; Didier Reignier

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 37, Issue: 3, page 451-478
- ISSN: 0764-583X

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topBerthon, Christophe, and Reignier, Didier. "An approximate nonlinear projection scheme for a combustion model." ESAIM: Mathematical Modelling and Numerical Analysis 37.3 (2010): 451-478. <http://eudml.org/doc/194173>.

@article{Berthon2010,

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.
},

author = {Berthon, Christophe, Reignier, Didier},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Hyperbolic systems in nonconservation form; finite volume methods; nonlinear projection method.; hyperbolic systems in nonconservation form; nonlinear projection method; turbulent flow; numerical results; convection-diffusion systems},

language = {eng},

month = {3},

number = {3},

pages = {451-478},

publisher = {EDP Sciences},

title = {An approximate nonlinear projection scheme for a combustion model},

url = {http://eudml.org/doc/194173},

volume = {37},

year = {2010},

}

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

DA - 2010/3//

PB - EDP Sciences

VL - 37

IS - 3

SP - 451

EP - 478

AB -
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.

LA - eng

KW - Hyperbolic systems in nonconservation form; finite volume methods; nonlinear projection method.; hyperbolic systems in nonconservation form; nonlinear projection method; turbulent flow; numerical results; convection-diffusion systems

UR - http://eudml.org/doc/194173

ER -

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