| Issue |
ESAIM: M2AN
Volume 56, Number 5, September-October 2022
|
|
|---|---|---|
| Page(s) | 1521 - 1544 | |
| DOI | https://doi.org/10.1051/m2an/2022049 | |
| Published online | 20 July 2022 | |
Computing effective diffusivities in 3D time-dependent chaotic flows with a convergent Lagrangian numerical method
1
Department of Statistics and CCAM, The University of Chicago, Chicago, IL 60637, USA
2
Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA
3
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, P.R. China
* Corresponding author: zhangzw@hku.hk
Received:
19
September
2021
Accepted:
11
May
2022
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 a structure-preserving scheme 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 chaotic 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.
Mathematics Subject Classification: 35B27 / 37A30 / 60H35 / 65M12 / 65M75
Key words: Convection-enhanced diffusion / time-dependent chaotic flows / effective diffusivity / structure-preserving scheme / convergence analysis
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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