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.
翻译:在本文中,我们研究与Kolmogorov-Petrovsky-Piskunov(KPP)无线性联系的时段细胞和混乱流的反扩散战线的传播速度。我们首先应用变式原则,将KPP前速的计算降低到一个具有定期域空间周期系数的线性反扩散操作员的主要电子价值问题。为此,我们开发了高效的Lagrangian粒子方法,通过Feynman-Kac公式计算主要电子价值。通过估计Feynman-Kac半组的趋同率和对线性对流溶解操作员的分解方法,我们获得了对拟议数字方法的趋同分析。最后,我们提出了数字结果,以证明在时段蜂窝和混乱流中计算KPP的前速度的拟议方法的准确性和效率,特别是基于时间的Arnold-Beltrami-Chilest(ABC)流和基于时空的Kolmoprov流。