A structure-preserving scheme for computing effective diffusivity and anomalous diffusion phenomena of random flows
Abstract
This paper aims to investigate the diffusion behavior of particles moving in stochastic flows under a structure-preserving scheme. We compute the effective diffusivity for normal diffusive random flows and establish the power law between spatial and temporal variables for cases with anomalous diffusion phenomena. From a Lagrangian approach, we separate the corresponding stochastic differential equations (SDEs) into sub-problems and construct a one-step structure-preserving method to solve them. Then by modified equation systems, the convergence analysis in calculating the effective diffusivity is provided and compared between the structure-preserving scheme and the Euler-Maruyama scheme. Also, we provide the error estimate for the structure-preserving scheme in calculating the power law for a series of super-diffusive random flows. Finally, we calculate the effective diffusivity and anomalous diffusion phenomena for a series of 2D and 3D random fields.
Keywords
Cite
@article{arxiv.2405.19003,
title = {A structure-preserving scheme for computing effective diffusivity and anomalous diffusion phenomena of random flows},
author = {Tan Zhang and Zhongjian Wang and Jack Xin and Zhiwen Zhang},
journal= {arXiv preprint arXiv:2405.19003},
year = {2024}
}
Comments
39pages, 10 figures, planning to submit for Journal of Scientific Computing or Numerische Mathematik