Computing effective diffusivities in 3D time-dependent chaotic flows with a convergent Lagrangian numerical method

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 differential equations (SDEs). Our is based on splitting method to solve corresponding SDEs deterministic subproblem discretized using while random Euler-Maruyama scheme. We obtain sharp and uniform-in-time proposed that allows us accurately compute long-time solutions SDEs. As such, can flows. Finally, present results demonstrate accuracy efficiency Arnold-Beltrami-Childress (ABC) flow Kolmogorov three-dimensional space.