Convergence analysis of a Lagrangian numerical scheme in computing effective diffusivity of 3D time-dependent flows

2021/06/02 by Wang, Zhongjian, Xin, Jack, Zhang, Zhiwen
#35B27 #37A30 #60H35 #65M12 #65M75 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2106.00953

Abstract

In this paper, we study the convergence analysis for a robust stochastic structure-preserving Lagrangian numerical scheme in computing effective diffusivity of time-dependent chaotic flows, which are modeled by stochastic differential equations (SDEs). Our numerical scheme is based on a splitting method to solve the corresponding SDEs in which the deterministic subproblem is discretized using structure-preserving schemes while the random subproblem is discretized using the Euler-Maruyama scheme. We obtain a sharp and uniform-in-time convergence analysis for the proposed numerical scheme that allows us to accurately compute long-time solutions of the SDEs. As such, we can compute the effective diffusivity for time-dependent flows. Finally, we present numerical results to demonstrate the accuracy and efficiency of the proposed method in computing effective diffusivity for the time-dependent Arnold-Beltrami-Childress (ABC) flow and Kolmogorov flow in three-dimensional space.

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