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Minimax Theory and its Applications 08 (2023), No. 1, 109--119
Copyright Heldermann Verlag 2023

Synchronized Front Propagation and Delayed Flame Quenching in Strain G-Equation and Time-Periodic Cellular Flows

Yu-Yu Liu
Department of Mathematics, National Cheng Kung University, Tainan, Taiwan

Jack Xin
Department of Mathematics, University of California, Irvine, U.S.A.

G-equations are level-set type Hamilton-Jacobi partial differential equations modeling propagation of flame front along a flow velocity and a laminar velocity. In consideration of flame stretching, strain rate may be added into the laminar speed. We perform finite difference computation of G-equations with the discretized strain term being monotone with respect to one-sided spatial derivatives. Let the flow velocity be the time-periodic cellular flow (modeling Rayleigh-Bénard advection), we compute the turbulent flame speeds as the asymptotic propagation speeds from a planar initial flame front. In strain G-equation model, front propagation is enhanced by the cellular flow, and flame quenching occurs if the flow intensity is large enough. In contrast to the results in steady cellular flow, front propagation in time periodic cellular flow may be locked into certain spatial-temporal periodicity pattern, and turbulent flame speed becomes a piecewise constant function of flow intensity. Also the disturbed flame front does not cease propagating until much larger flow intensity.

Keywords: G-equations, cellular flows, turbulent flame speeds, synchronization, flame quenching.

MSC: 70H20, 76F25, 76M20.

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