A convergent interacting particle method and computation of KPP front speeds in chaotic flows. (English) Zbl 07538279
Summary: In this paper, we study the propagation speeds of reaction-diffusion-advection 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 coefficient 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 method for approximating the linear advection-diffusion solution operators, we obtain convergence analysis for the proposed numerical method. 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 flow and time-dependent Kolmogorov flow in three-dimensional space.
MSC:
| 65-XX | Numerical analysis |
| 35K57 | Reaction-diffusion equations |
| 47D08 | Schrödinger and Feynman-Kac semigroups |
| 65C35 | Stochastic particle methods |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
Keywords:
KPP front speeds; cellular and chaotic flows; Feynman-Kac semigroups; interacting particle method; eigenvalue problems; convergence analysisReferences:
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