  In this paper, we study the propagation speeds of
reaction-diffusion-advection (RDA) fronts in time-periodic cellular and chaotic
flows with Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity. We first apply the
variational principle to reduce the computation of KPP front speeds to a
principal eigenvalue problem of a linear advection-diffusion operator with
space-time periodic coefficients on a periodic domain. To this end, we develop
efficient Lagrangian particle methods to compute the principal eigenvalue
through the Feynman-Kac formula. By estimating the convergence rate of
Feynman-Kac semigroups and the operator splitting methods for approximating the
linear advection-diffusion solution operators, we obtain convergence analysis
for the proposed numerical methods. Finally, we present numerical results to
demonstrate the accuracy and efficiency of the proposed method in computing KPP
front speeds in time-periodic cellular and chaotic flows, especially the
time-dependent Arnold-Beltrami-Childress (ABC) flow and time-dependent
Kolmogorov flow in three-dimensional space.
