Two level homogenization of flows in deforming double porosity media: biot-darcy-brinkman model
Year: 2017
Type: conference-paper
Abstract: We present the two-level homogenization of the flow in a deformable double-porous structure described at two characteristic scales: the higher level porosity associated with the mesoscopic structure is constituted by channels in an elastic skeleton which is made of a microporous material. The macroscopic model is derived by the asymptotic analysis of the viscous flow in the heterogeneous structure characterized by two small parameters. The first level upscaling yields a Biot continuum model coupled with the Stokes flow. The second step of the homogenization leads to a macroscopic flow model which attains the form of the Darcy-Brinkman flow model coupled with the deformation of the poroelastic continuum involving the effective parameters given by the microscopic and the mesoscopic porosity features.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3014515085