Calculating effective diffusivities in the limit of vanishing molecular diffusion
Abstract
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 time-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 Euler-based integrators. Various asymptotic limits of physical interest are investigated by means of numerical experiments, using the new integrators.
Additional Information
© 2008 Elsevier. Received 19 June 2008; Received in revised form 9 October 2008; Accepted 10 October 2008; Available online 22 October 2008. The authors thank the Center for Scientific Computing at Warwick University for computational resources. K.C.Z was supported by Warwick University through the Warwick Postgraduate Research Fellowship (WPRF) and by the EPSRC.Attached Files
Submitted - 0806.3403.pdf
Files
Name | Size | Download all |
---|---|---|
md5:532ba757ef8eb982f0599f655517c9e7
|
1.1 MB | Preview Download |
Additional details
- Eprint ID
- 69494
- DOI
- 10.1016/j.jcp.2008.10.014
- Resolver ID
- CaltechAUTHORS:20160805-155749338
- Warwick University
- Engineering and Physical Sciences Research Council (EPSRC)
- Created
-
2016-08-05Created from EPrint's datestamp field
- Updated
-
2021-11-11Created from EPrint's last_modified field
- Other Numbering System Name
- Andrew Stuart
- Other Numbering System Identifier
- J75