Math. Model. Nat. Phenom.
Volume 8, Number 3, 2013Front Propagation
|Page(s)||198 - 205|
|Published online||12 June 2013|
Turbulent Flame Speeds of G-equation Models in Unsteady Cellular Flows
1 Department of Mathematics, National
Cheng Kung University, Tainan
2 Department of Mathematics, University of California, Irvine, CA 92697, USA
⋆ Corresponding author. E-mail: firstname.lastname@example.org
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.
Mathematics Subject Classification: 70H20 / 76F25 / 76M20
Key words: G-equations / front speed computation / cellular flows / frequency locking
© EDP Sciences, 2013
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