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

Yu-Yu Liu,Jack Xin

Minimax theory and its applications, Tome 8 (2023) no. 1

Résumé

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.

Détail

Mots-clés : G-equations, cellular flows, turbulent flame speeds, synchronization, flame quenching. 2010 Mathematics Subject Classification: 70H20, 76F25, 76M20