Calculating effective diffusivities in the limit of vanishing molecular diffusion

JOURNAL OF COMPUTATIONAL PHYSICS

卷:228

Article

Pavliotis, G. A.¹  Stuart, A. M.²  Zygalakis, K. C.² 

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[2] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

关键词: Homogenization theory;    Multiscale analysis;    Monte Carlo methods;    Passive tracers;    Inertial particles;    Effective diffusivity;   

DOI  :  10.1016/j.jcp.2008.10.014

来源: Elsevier

【 摘 要 】

In this paper we study the problem of the numerical calculation (by Monte Carlo methods) of the effective diffusivity for a particle moving in a periodic divergent-free velocity field, in the limit of vanishing molecular diffusion. In this limit traditional numerical methods typically fail, since they do not represent accurately the geometry of the underlying deterministic dynamics. We propose a stochastic splitting method that takes into account the volume-preserving property of the equations of motion in the absence of noise, and when inertial effects can be neglected. An extension of the method is then proposed for the cases where the noise has a non-trivial tune-correlation structure and when inertial effects cannot be neglected. The method of modified equations is used to explain failings of Euler-based methods. The new stochastic geometric integrators are shown to outperform standard Etder-based integrators. Various asymptotic limits of physical interest are investigated by means of numerical experiments, using the new integrators. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free