Thermal flows in fractured porous media
Isabelle Gruais, Dan Poliševski · ESAIM Mathematical Modelling and Numerical Analysis · 2021
We consider the thermal flow problem occuring in a fractured porous medium. The incompressible filtration flow in the porous matrix and the viscous flow in the fractures obey the Boussinesq approximation of Darcy-Forchheimer law and respectively, the Stokes system. They are coupled by the Saffman’s variant of the Beavers–Joseph condition. Existence and uniqueness properties are presented. The use of the energy norm in describing the Darcy-Forchheimer law proves to be appropriate. In theε-periodic framework, we find the two-scale homogenized system which governs their asymptotic behaviours whenε→ 0 and the Forchheimer effect vanishes. The limit problem is mainly a model of two coupled thermal flows, neither of them being incompressible.