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In this paper, we study the convergence analysis for a robust stochasticstructure-preserving Lagrangian numerical scheme in computing effectivediffusivity of time-dependent chaotic flows, which are modeled by stochasticdifferential equations (SDEs). Our numerical scheme is based on a splittingmethod to solve the corresponding SDEs in which the deterministic subproblem isdiscretized using structure-preserving schemes while the random subproblem isdiscretized using the Euler-Maruyama scheme. We obtain a sharp anduniform-in-time convergence analysis for the proposed numerical scheme thatallows us to accurately compute long-time solutions of the SDEs. As such, wecan compute the effective diffusivity for time-dependent flows. Finally, wepresent numerical results to demonstrate the accuracy and efficiency of theproposed method in computing effective diffusivity for the time-dependentArnold-Beltrami-Childress (ABC) flow and Kolmogorov flow in three-dimensionalspace.

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