Published

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

Penghe Zu, Long Chen, and Jack Xin

Physica D: Nonlinear Phenomena, 311, 37 - 44, 2015

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ABSTRACT:

 The minimal speeds (c) of the Kolmogorov-Petrovsky-Piskunov
  (KPP) fronts at small diffusion (epsilon << 1) in a class of
  time-periodic cellular flows with chaotic streamlines is
  investigated in this paper. The variational principal of c reduces
  the computation to that of a principal eigenvalue problem on a
  periodic domain of a linear advection-diffusion operator with
  space-time periodic coefficients and small diffusion. To solve the
  advection dominated time-dependent eigenvalue problem efficiently
  over large time, a combination of finite element and spectral
  methods, as well as the associated fast solvers, are utilized to
  accelerate computation. In contrast to the scaling c =
  O(epsilon^(1/4)) in steady cellular flows, a new relation c = O(1)
  as epsilon << 1 is revealed in the time-periodic cellular flows due
  to the presence of chaotic streamlines. Residual propagation speed
  emerges from the Lagrangian chaos which is quantified as a
  sub-diffusion process.