A Domain Decomposition Approach to Finite-Epsilon Homogenization of Scalar Transport in Porous Media
| Autor: | Michel Quintard, Yohan Davit, Jean-Claude Latché, Fabrice Golfier |
|---|---|
| Přispěvatelé: | Institut de mécanique des fluides de Toulouse (IMFT), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées, GeoRessources, Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre de recherches sur la géologie des matières premières minérales et énergétiques (CREGU)-Institut national des sciences de l'Univers (INSU - CNRS), Institut de Radioprotection et de Sûreté Nucléaire (IRSN), Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Institut de Radioprotection et de Sûreté Nucléaire - IRSN (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Centre de Recherches sur la Géologie des Matières Minérales et Énergétiques - CREGU (FRANCE), Université de Lorraine (FRANCE) |
| Rok vydání: | 2019 |
| Předmět: |
010504 meteorology & atmospheric sciences
Mécanique des fluides Porous media 0207 environmental engineering 02 engineering and technology 01 natural sciences Homogenization (chemistry) Domain decomposition [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] Statistical physics 020701 environmental engineering Non-Fickian Microscale chemistry 0105 earth and related environmental sciences Physics Partial differential equation Advection Applied Mathematics A domain Domain decomposition methods Decomposition Porous medium Scalar transport Advection and diffusion Spatial averaging |
| Zdroj: | SIAM Journal on Applied Mathematics SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2019, 79 (5), pp.1797-1822. ⟨10.1137/17M1157775⟩ |
| ISSN: | 1095-712X 0036-1399 |
| DOI: | 10.1137/17m1157775 |
| Popis: | International audience; Modeling scalar transport by advection and diffusion in multiscale porous structures is a challenging problem, particularly in the preasymptotic regimes when non-Fickian effects are prominent. Mathematically, one of the main difficulties is to obtain macroscale models from the homogenization of conservation equations at microscale when epsilon, the ratio of characteristic lengthscales between the micro- and macroscale, is not extremely small compared to unity. Here, we propose the basis of a mathematical framework to do so. The focal idea is to decompose the spatial domain at pore-scale into a set of N subdomains to capture characteristic times associated with exchanges between these subdomains. At macroscale, the corresponding representation consists of a system of N coupled partial differential equations describing the transport of the spatially averaged scalar variable within each subdomain. Besides constructing the framework, we also compare numerically the results of our models to a complete resolution of the problem at the pore-scale, which shows great promises for capturing preasymptotic regimes, non-Fickian transport, and going toward finite-epsilon homogenization. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|