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Turbulent Flame Speeds of G-equation Models in Unsteady Cellular Flows

Published online by Cambridge University Press:  12 June 2013

Y-Y Liu ,
J. Xin  and
Y. Yu
Y-Y Liu*
Affiliation:
Department of Mathematics, National Cheng Kung University, Tainan 70101, Taiwan
J. Xin
Affiliation:
Department of Mathematics, University of California, Irvine, CA 92697, USA
Y. Yu
Affiliation:
Department of Mathematics, University of California, Irvine, CA 92697, USA
*
⋆ Corresponding author. E-mail: yuyul@ncku.edu.tw
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Abstract

We perform a computationl study of front speeds of G-equation models in time dependent cellular flows. The G-equations arise in premixed turbulent combustion, and are Hamilton-Jacobi type level set partial differential equations (PDEs). The curvature-strain G-equations are also non-convex with degenerate diffusion. The computation is based on monotone finite difference discretization and weighted essentially nonoscillatory (WENO) methods. We found that the large time front speeds lock into the frequency of time periodic cellular flows in curvature-strain G-equations similar to what occurs in the basic inviscid G-equation. However, such frequency locking phenomenon disappears in viscous G-equation, and in the inviscid G-equation if time periodic oscillation of the cellular flow is replaced by time stochastic oscillation.

Keywords

G-equationsfront speed computationcellular flowsfrequency locking
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 3: Front Propagation , 2013 , pp. 198 - 205
Copyright
© EDP Sciences, 2013

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