|
ISSN: 1543-1649 Print
ISSN: 1940-4352 Online
|
|
|
|
| |
You can order a single issue or an individual article, as well as view the table of contents or article abstract by clicking on the volume number, then the issue number in the right sidebar.
|
|
|
|
|
|
Institutional price: $1197.00
|
|
Online subscription
|
|
DOI: 10.1615/IntJMultCompEng.v6.i4
Pages: 115
|
DOI: 10.1615/IntJMultCompEng.v6.i4.10
|
Article price - $35.00 |
 |
Wavelet-Based Spatial Scaling of Coupled Reaction-Diffusion Fields
Sudib K. Mishra
Department of Civil Engineering and Engineering Mechanics, University of Arizona, P.O. Box 210072, University of Arizona, Tucson, Arizona 85721, USA
Krishna Muralidharan
Department of Material Science and Engineering, University of Arizona, Tucson, Arizona 85721, USA
Pierre A. Deymier
Department of Material Science and Engineering, University of Arizona, Tucson, Arizona 85721, USA
George Frantziskonis
Department of Civil Engineering and Engineering Mechanics, and Department of Material Science and Engineering, University of Arizona, USA
Sreekanth Pannala
Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA
Srdjan Simunovic
Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA
ABSTRACT
Multiscale schemes for transferring information from fine to coarse scales are typically based on homogenization techniques. Such schemes smooth the fine scale features of the underlying fields, often resulting in the inability to accurately retain the fine scale correlations. In addition, higher-order statistical moments (beyond mean) of the relevant field variables are not necessarily preserved. As a superior alternative to averaging homogenization methods, a wavelet-based scheme for the exchange of information between a reactive and diffusive field in the context of multiscale reaction-diffusion problems is proposed and analyzed. The scheme is shown to be efficient in passing information along scales, from fine to coarse, i.e., upscaling as well as from coarse to fine, i.e., downscaling. It incorporates fine scale statistics (higher-order moments beyond mean), mainly due to the capability of wavelets to represent fields hierarchically. Critical to the success of the scheme is the identification of dominant scales containing the majority of the useful information. The dominant scales in effect specify the coarsest resolution possible. The scheme is applied in detail to the analysis of a diffusive system with a chemically reacting boundary. Reactions are simulated using kinetic Monte Carlo (kMC) and diffusion is solved by finite differences (FDs). Spatial scale differences are present at the interface of the kMC sites and the diffusion grid. The computational efficiency of the scheme is compared to results obtained by averaging homogenization, and to results from a benchmark scheme that ensures spatial scale parity between kMC and FD.
pages 281-297
|
