Publication de 6 numéros par an
ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352
IF:
1.4
5-Year IF:
1.3
Immediacy Index:
2.2
Eigenfactor:
0.00034
JCI:
0.46
SJR:
0.333
SNIP:
0.606
CiteScore™::
3.1
H-Index:
31
Indexed in
Wavelet-Based Spatial Scaling of Coupled Reaction-Diffusion Fields
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RÉSUMÉ
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.
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Scheibe Timothy D., Murphy Ellyn M., Chen Xingyuan, Rice Amy K., Carroll Kenneth C., Palmer Bruce J., Tartakovsky Alexandre M., Battiato Ilenia, Wood Brian D., An Analysis Platform for Multiscale Hydrogeologic Modeling with Emphasis on Hybrid Multiscale Methods, Groundwater, 53, 1, 2015. Crossref
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Zheng Xiaoming, Kim Yeonhyang, Rakesh Leela, Lin En-Bing, A conservative and variation preserving finite volume method for non-overlapping meshes of reaction and diffusion in angiogenesis, Journal of Computational and Applied Mathematics, 275, 2015. Crossref
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Gur Sourav, Danielson Thomas, Xiong Qingang, Hin Celine, Pannala Sreekanth, Frantziskonis George, Savara Aditya, Daw C. Stuart, Wavelet-based surrogate time series for multiscale simulation of heterogeneous catalysis, Chemical Engineering Science, 144, 2016. Crossref
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Zheng Xiaoyang, Wei Zhengyuan, Discontinuous Legendre wavelet Galerkin method for reaction–diffusion equation, International Journal of Computer Mathematics, 94, 9, 2017. Crossref
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Gur Sourav, Frantziskonis George N, Linking simulations and experiments for the multiscale tracking of thermally induced martensitic phase transformation in NiTi SMA, Modelling and Simulation in Materials Science and Engineering, 24, 7, 2016. Crossref
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Frantziskonis George N, Gur Sourav, Length scale effects and multiscale modeling of thermally induced phase transformation kinetics in NiTi SMA, Modelling and Simulation in Materials Science and Engineering, 25, 4, 2017. Crossref
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Gur Sourav, Frantziskonis George N., Pannala Sreekanth, Daw C. Stuart, Application of Wavelet-Based Methods for Accelerating Multi-Time-Scale Simulation of Bistable Heterogeneous Catalysis, Industrial & Engineering Chemistry Research, 56, 9, 2017. Crossref