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We aim to efficiently compute spreading speeds ofreaction-diffusion-advection (RDA) fronts in divergence free random flows underthe Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity. We study a stochasticinteracting particle method (IPM) for the reduced principal eigenvalue(Lyapunov exponent) problem of an associated linear advection-diffusionoperator with spatially random coefficients. The Fourier representation of therandom advection field and the Feynman-Kac (FK) formula of the principaleigenvalue (Lyapunov exponent) form the foundation of our method implemented asa genetic evolution algorithm. The particles undergo advection-diffusion, andmutation/selection through a fitness function originated in the FK semigroup.We analyze convergence of the algorithm based on operator splitting, presentnumerical results on representative flows such as 2D cellular flow and 3DArnold-Beltrami-Childress (ABC) flow under random perturbations. The 2Dexamples serve as a consistency check with semi-Lagrangian computation. The 3Dresults demonstrate that IPM, being mesh free and self-adaptive, is simple toimplement and efficient for computing front spreading speeds in theadvection-dominated regime for high-dimensional random flows on unboundeddomains where no truncation is needed.

A convergent interacting particle method for computing KPP front speeds in random flows