
Minimax Theory and its Applications 08 (2023), No. 1, 109119 Copyright Heldermann Verlag 2023 Synchronized Front Propagation and Delayed Flame Quenching in Strain GEquation and TimePeriodic Cellular Flows YuYu Liu Department of Mathematics, National Cheng Kung University, Tainan, Taiwan yuyul@ncku.edu.tw Jack Xin Department of Mathematics, University of California, Irvine, U.S.A. jxin@math.uci.edu Gequations are levelset type HamiltonJacobi 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 Gequations with the discretized strain term being monotone with respect to onesided spatial derivatives. Let the flow velocity be the timeperiodic cellular flow (modeling RayleighBénard advection), we compute the turbulent flame speeds as the asymptotic propagation speeds from a planar initial flame front. In strain Gequation 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 spatialtemporal 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: Gequations, cellular flows, turbulent flame speeds, synchronization, flame quenching. MSC: 70H20, 76F25, 76M20. [ Fulltextpdf (656 KB)] for subscribers only. 