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In this paper, we propose stochastic structure-preserving schemes to computethe effective diffusivity for particles moving in random flows. We firstintroduce the motion of particles using the Lagrangian formulation, which ismodeled by stochastic differential equations (SDEs). We also discuss thedefinition of the corrector problem and effective diffusivity. Then we proposestochastic structure-preserving schemes to solve the SDEs and provide a sharpconvergence analysis for the numerical schemes in computing effectivediffusivity. The convergence analysis follows a probabilistic approach, whichinterprets the solution process generated by our numerical schemes as a Markovprocess. By using the central limit theorem for the solution process, we obtainthe convergence analysis of our method in computing long time solutions. Mostimportantly our convergence analysis reveals the connection of discrete-typeand continuous-type corrector problems, which is fundamental and interesting.We present numerical results to demonstrate the accuracy and efficiency of theproposed method and investigate the convection-enhanced diffusion phenomenon intwo- and three-dimensional incompressible random flows.

Convergence of stochastic structure-preserving schemes for computing effective diffusivity in random flows