Paper Info
Title
Numerical Studies of Homogenization under a Fast Cellular Flow.
Abstract
We consider a two dimensional particle diffusing in the presence of a fast cellular flow confined to a finite domain. If the flow amplitude A is held fixed and the number of cells L-2 -> infinity, then the problem homogenizes; this has been well studied. Also well studied is the limit when L is fixed and A -> infinity. In this case the solution averages along stream lines. The double limit as both the flow amplitude A -> infinity and the number of cells L-2 -> infinity was recently studied [G. Iyer et al., preprint, arXiv:1108.0074]; one observes a sharp transition between the homogenization and averaging regimes occurring at A approximate to L-4. This paper numerically studies a few theoretically unresolved aspects of this problem when both A and L are large that were left open in [G. Iyer et al., preprint, arXiv:1108.0074] using the numerical method devised in [G. A. Pavliotis, A. M. Stewart, and K. C. Zygalakis, J. Comput. Phys., 228 (2009), pp. 1030-1055]. Our treatment of the numerical method uses recent developments in the theory of modified equations for numerical integrators of stochastic differential equations [K. C. Zygalakis, SIAM J. Sci. Comput., 33 (2001), pp. 102-130].
Year
DOI
Venue
2012
10.1137/120861308
MULTISCALE MODELING & SIMULATION
Keywords
Field
DocType
homogenization,averaging,backward error analysis,Monte Carlo methods
Monte Carlo method,Approx,Mathematical analysis,Homogenization (chemistry),Flow (psychology),Numerical analysis,Amplitude,Mathematics,Preprint
Journal
Volume
Issue
ISSN
10
3
1540-3459
Citations 
PageRank 
References 
0
0.34
4
Authors
2
Name
Order
Citations
PageRank
Gautam Iyer112.04
Konstantinos C. Zygalakis2488.27