一种收敛的相互作用粒子方法及混沌流中KPP波前速度的计算
A convergent interacting particle method and computation of KPP front speeds in chaotic flows
摘要：
本文研究了具有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（RDA）前沿的传播速度。我们首先应用变分原理将KPP波前速度的计算归结为周期域上具有时空周期系数的线性平流-扩散算子的主本征值问题。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，得到了所提出的数值方法的收敛性分析.最后，通过数值实验验证了该方法在计算时间周期细胞流和混沌流，特别是三维时间相关Arnold-Beltrami-Childress（ABC）流和时间相关Kolmogorov流的KPP波前速度时的准确性和有效性.
英文摘要：
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.
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