2021/03/27 by Junlong Lyu, Lyu, Junlong, Zhongjian Wang +5 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #35K57 #47D08 #65C35 #65L20 #65N25 #Cellular Automata and Applications #FOS: Mathematics #Numerical Analysis (math.NA) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2103.14796
openalex publication_date 2021/03/27 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
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.