Numerical Studies of Homogenization under a Fast Cellular Flow

Handle URI:
http://hdl.handle.net/10754/599022
Title:
Numerical Studies of Homogenization under a Fast Cellular Flow
Authors:
Iyer, Gautam; Zygalakis, Konstantinos C.
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 →∞, then the problem homogenizes; this has been well studied. Also well studied is the limit when L is fixed and A→∞. In this case the solution averages along stream lines. The double limit as both the flow amplitude A→∞and the number of cells L 2 →∞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 = L 2. 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]. © 2012 Society for Industrial and Applied Mathematics.
Citation:
Iyer G, Zygalakis KC (2012) Numerical Studies of Homogenization under a Fast Cellular Flow. Multiscale Model Simul 10: 1046–1058. Available: http://dx.doi.org/10.1137/120861308.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
Multiscale Modeling & Simulation
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
13-Sep-2012
DOI:
10.1137/120861308
Type:
Article
ISSN:
1540-3459; 1540-3467
Sponsors:
This work was partially supported by the Center for Nonlinear Analysis (NSF DMS-0405343 and DMS-0635983) and NSF PIRE grant OISE 0967140.This author's research was partially supported by NSF-DMS 1007914.This author's research was partially supported by award KUK-C1-013-04 of the King Abdullah University of Science and Technology (KAUST). It was partially carried out at Carnegie Mellon University, whose hospitality is gratefully acknowledged.
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Full metadata record

DC FieldValue Language
dc.contributor.authorIyer, Gautamen
dc.contributor.authorZygalakis, Konstantinos C.en
dc.date.accessioned2016-02-25T13:51:21Zen
dc.date.available2016-02-25T13:51:21Zen
dc.date.issued2012-09-13en
dc.identifier.citationIyer G, Zygalakis KC (2012) Numerical Studies of Homogenization under a Fast Cellular Flow. Multiscale Model Simul 10: 1046–1058. Available: http://dx.doi.org/10.1137/120861308.en
dc.identifier.issn1540-3459en
dc.identifier.issn1540-3467en
dc.identifier.doi10.1137/120861308en
dc.identifier.urihttp://hdl.handle.net/10754/599022en
dc.description.abstractWe 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 →∞, then the problem homogenizes; this has been well studied. Also well studied is the limit when L is fixed and A→∞. In this case the solution averages along stream lines. The double limit as both the flow amplitude A→∞and the number of cells L 2 →∞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 = L 2. 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]. © 2012 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis work was partially supported by the Center for Nonlinear Analysis (NSF DMS-0405343 and DMS-0635983) and NSF PIRE grant OISE 0967140.This author's research was partially supported by NSF-DMS 1007914.This author's research was partially supported by award KUK-C1-013-04 of the King Abdullah University of Science and Technology (KAUST). It was partially carried out at Carnegie Mellon University, whose hospitality is gratefully acknowledged.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectAveragingen
dc.subjectBackward error analysisen
dc.subjectHomogenizationen
dc.subjectMonte Carlo methodsen
dc.titleNumerical Studies of Homogenization under a Fast Cellular Flowen
dc.typeArticleen
dc.identifier.journalMultiscale Modeling & Simulationen
dc.contributor.institutionCarnegie Mellon University, Pittsburgh, United Statesen
dc.contributor.institutionUniversity of Southampton, Southampton, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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