SIAM Journal on Numerical Analysis, Volume 60, Issue 3, Page 1136-1167, June 2022.
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.

中文翻译：

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混沌流中KPP前沿速度的收敛相互作用粒子法和计算

SIAM 数值分析杂志，第 60 卷，第 3 期，第 1136-1167 页，2022 年 6 月。
在本文中，我们研究了具有 Kolmogorov--Petrovsky--Piskunov (KPP) 非线性的时间周期细胞流和混沌流中反应-扩散-平流前沿的传播速度。我们首先应用变分原理将 KPP 前沿速度的计算简化为在周期域上具有时空周期系数的线性对流-扩散算子的主特征值问题。为此，我们开发了有效的拉格朗日粒子方法，通过 Feynman--Kac 公式计算主特征值。通过估计Feynman--Kac半群的收敛速度和近似线性对流-扩散解算子的算子分裂方法，我们得到了所提出数值方法的收敛性分析。最后，