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Höfer, Richard M.

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

DokumentenartArtikel
Titel eines Journals oder einer ZeitschriftNonlinearity
Verlag:IOP Publishing Ltd
Ort der Veröffentlichung:BRISTOL
Band:36
Nummer des Zeitschriftenheftes oder des Kapitels:11
Seitenbereich:S. 6019-6046
Datum10 Oktober 2023
InstitutionenMathematik
Identifikationsnummer
WertTyp
10.1088/1361-6544/acfe56DOI
Stichwörter / KeywordsINCOMPRESSIBLE-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-Klassifikation500 Naturwissenschaften und Mathematik > 510 Mathematik
StatusVeröffentlicht
BegutachtetJa, diese Version wurde begutachtet
An der Universität Regensburg entstandenJa
URN der UB Regensburgurn:nbn:de:bvb:355-epub-549026
Dokumenten-ID54902

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