Convergence analysis of a Lagrangian numerical scheme in computing effective diffusivity of 3D time-dependent flows
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.
Keywords
Cite
@article{arxiv.2106.00953,
title = {Convergence analysis of a Lagrangian numerical scheme in computing effective diffusivity of 3D time-dependent flows},
author = {Zhongjian Wang and Jack Xin and Zhiwen Zhang},
journal= {arXiv preprint arXiv:2106.00953},
year = {2021}
}
Comments
arXiv admin note: text overlap with arXiv:1808.06309