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

Abstract

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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.

How to cite

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Berthon, 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 -

References

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