Höfer, Richard M. (2023) Homogenization of the Navier-Stokes equations in perforated domains in the inviscid limit. NONLINEARITY, 36 (11). pp. 6019-6046. ISSN 0951-7715, 1361-6544
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled 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 |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 21 Feb 2024 10:48 |
| Last Modified: | 21 Feb 2024 10:48 |
| URI: | https://pred.uni-regensburg.de/id/eprint/58927 |
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