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The minimal speeds ($c^*$) of the Kolmogorov-Petrovsky-Piskunov (KPP) frontsat small diffusion ($\epsilon \ll 1$) in a class of time-periodic cellularflows with chaotic streamlines is investigated in this paper. The variationalprinciple of $c^*$ reduces the computation to that of a principal eigenvalueproblem on a periodic domain of a linear advection-diffusion operator withspace-time periodic coefficients and small diffusion. To solve the advectiondominated time-dependent eigenvalue problem efficiently over large time, acombination of finite element and spectral methods, as well as the associatedfast solvers, are utilized to accelerate computation. In contrast to thescaling $c^*=\mathcal{O}(\epsilon^{1/4})$ in steady cellular flows, a newrelation $c^* = \mathcal{O}(1)$ as $\epsilon \ll 1$ is revealed in thetime-periodic cellular flows due to the presence of chaotic streamlines.Residual propagation speed emerges from the Lagrangian chaos which isquantified as a sub-diffusion process.

A Computational Study of Residual KPP Front Speeds in Time-Periodic Cellular Flows in the Small Diffusion Limit