Fluid flow and deformation in composite porous media.

摘要

The Biot model of fluid flow in a deformable saturated porous media in the three dimensional case is developed. This model is extended to a system of partial differential equations representing diffusion through a composite elastic medium. Existence, uniqueness and regularity theory is developed for the initial-boundary-value problem in the quasi-static case. This system is resolved for both strong and weak notions of solution as a linear implicit evolution equation in suitable Hilbert space. A numerical example is presented in order to demonstrate the significance of the coupling of the diffusion and deformation.