The Transition Between the Navier–Stokes Equations to the Darcy Equation in a Thin Porous Medium
We consider a Newtonian flow in a thin porous medium Ωε of thickness ε which is perforated by periodically distributed solid cylinders of size aε. Generalizing [2], the fluid is described by the 3D incompressible Navier-Stokes system where the external force takes values in the space H^{−1}, and the...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/157536 |
| Acceso en línea: | https://hdl.handle.net/11441/157536 https://doi.org/10.1007/s00009-018-1086-z |
| Access Level: | acceso abierto |
| Palabra clave: | Homogenization Navier-Stokes equations Darcy’s law porous medium thin-film fluids. |
| Sumario: | We consider a Newtonian flow in a thin porous medium Ωε of thickness ε which is perforated by periodically distributed solid cylinders of size aε. Generalizing [2], the fluid is described by the 3D incompressible Navier-Stokes system where the external force takes values in the space H^{−1}, and the porous medium considered has one of the most commonly used distribution of cylinders: hexagonal distribution. By means of an adaptation of the unfolding method, three different Darcy’s laws are rigorously derived from this model depending on the magnitude aε with respect to ε. |
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