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Asymptotic expansion for a flow in a periodic porous medium. (English. Abridged French version) Zbl 0896.76090

Summary: We consider a fluid flow in a porous medium \(\Omega_\varepsilon\) with a characteristic pore size \(\varepsilon\). Starting from the Navier-Stokes equations on the microscopic level and using the homogenization method, we find corrections of the classical Darcy’s law governing the macroscopic flow.

MSC:

76S05 Flows in porous media; filtration; seepage
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
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