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المؤلفون: Lakkis, Omar, Muntean, Adrian, 1974, Richardson, Omar, Venkataraman, Chandrasekhar
المصدر: GAMM Mitteilungen. 47(4)
مصطلحات موضوعية: computational efficiency, finite elements, multiscale modeling, varying microstructures1 INTRODUCTIONModels involving transport and diffusion phenomena interacting at multiple scales (multiscale) are ubiquitous in thenatural sciences and engineering [52]. Multiscale modeling is a key tool for developing effective techniques to describethese phenomena, which may otherwise be computationally intractable. Specifically, assuming scale-separation in mod-els allows us to examine the interplay between processes active on vastly different length and time scales, defining, forexample, phenomena on macroscales and microscales [13, 53]. In most practically relevant cases, the microscalesare active in the sense that they are hosting localized phase transitions described mathematically by moving interfaceswith a priori known or unknown velocities. The case of known interface velocities is both mathematically and computa-tionally well-understood (cf. e.g., [10]), while the case of unknown interface velocities is still a matter of concern, compare[11, 55] for some very recent asymptotic analysis results concerning closely related reaction-diffusion scenarioswhich arise in the context of reactive transport in porous media.Here, we consider a flow process that takes place on two distinct physical scales. In the simplest setting, we canidentify a macroscopic scale where a model governs the behavior of a (macroscopic) fluid in which averages over theThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided theoriginal work is properly cited.© 2024 The Authors. GAMM - Mitteilungen published by Wiley-VCH GmbH.GAMM - Mitteilungen. 2024, 47:e202470005. wileyonlinelibrary.com/journal/gamm 1 of 18https://doi.org/10.1002/gamm.202470005, Matematik, Mathematics
وصف الملف: electronic