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Homogenization of the Navier–Stokes equations in perforated domains in the inviscid limit
Höfer, Richard M.
(2023)
Homogenization of the Navier–Stokes equations in perforated domains in the inviscid limit.
Nonlinearity 36 (11), S. 6019-6046.
Veröffentlichungsdatum dieses Volltextes: 23 Okt 2023 07:30
Artikel
DOI zum Zitieren dieses Dokuments: 10.5283/epub.54902
Zusammenfassung
We study the solution u(epsilon) to the Navier-Stokes equations in perforated by small particles centered at with no-slip boundary conditions at the particles. We study the behavior of u(epsilon) for small epsilon, depending on the diameter epsilon(alpha), alpha > 1, of the particles and the viscosity epsilon(gamma), gamma > 0, of the fluid. We prove quantitative convergence results for ...
We study the solution u(epsilon) to the Navier-Stokes equations in perforated by small particles centered at with no-slip boundary conditions at the particles. We study the behavior of u(epsilon) for small epsilon, depending on the diameter epsilon(alpha), alpha > 1, of the particles and the viscosity epsilon(gamma), gamma > 0, of the fluid. We prove quantitative convergence results for u(epsilon) in all regimes when the local Reynolds number at the particles is negligible. Then, the particles approximately exert a linear friction force on the fluid. The obtained effective macroscopic equations depend on the order of magnitude of the collective friction. We obtain (a) the Euler-Brinkman equations in the critical regime, (b) the Euler equations in the subcritical regime and (c) Darcy's law in the supercritical regime.
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Details
| Dokumentenart | Artikel | ||||
| Titel eines Journals oder einer Zeitschrift | Nonlinearity | ||||
| Verlag: | IOP Publishing Ltd | ||||
|---|---|---|---|---|---|
| Ort der Veröffentlichung: | BRISTOL | ||||
| Band: | 36 | ||||
| Nummer des Zeitschriftenheftes oder des Kapitels: | 11 | ||||
| Seitenbereich: | S. 6019-6046 | ||||
| Datum | 10 Oktober 2023 | ||||
| Institutionen | Mathematik | ||||
| Identifikationsnummer |
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| Stichwörter / Keywords | INCOMPRESSIBLE-FLOW; DIVERGENCE OPERATOR; VOLUME DISTRIBUTION; TINY HOLES; FLUID-FLOW; VISCOSITY; EULER; DERIVATION; PARTICLES; LAW; homogenization; perforated domain; Navier-Stokes equations; inviscid limit; Euler equations; Darcy's law; Euler-Brinkman equations | ||||
| Dewey-Dezimal-Klassifikation | 500 Naturwissenschaften und Mathematik > 510 Mathematik | ||||
| Status | Veröffentlicht | ||||
| Begutachtet | Ja, diese Version wurde begutachtet | ||||
| An der Universität Regensburg entstanden | Ja | ||||
| URN der UB Regensburg | urn:nbn:de:bvb:355-epub-549026 | ||||
| Dokumenten-ID | 54902 |
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