A Convergent Interacting Particle Method and Computation of KPP Front Speeds in Chaotic Flows

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 variational principle to reduce computation KPP front a principal eigenvalue problem linear advection-diffusion operator space-time periodic coefficients on domain. To end, develop efficient Lagrangian particle methods compute through Feynman-Kac formula. By estimating convergence rate semigroups splitting for approximating solution operators, obtain analysis proposed numerical methods. Finally, present results demonstrate accuracy efficiency method computing flows, especially time-dependent Arnold-Beltrami-Childress (ABC) flow Kolmogorov three-dimensional space.