Darcy's law for a compressible thermofluid

Abstract

A linear system of differential equations describing a joint motion of a thermoelastic porous body with a sufficiently large Lamé's constants (absolutelty rigid body) and a thermofluid, occupying porous space, is considered. The rigorous justification, under various conditions imposed on physical parameters, is fulfilled for homogenization procedures as the dimensionless size of the pores tends to zero, while the porous body is geometrically periodic. As the results we derive Darcy's system of filtration or acoustic equations for thermofluid, depending on ratios between physical parameters. The proofs are based on Nguetseng's two-scale convergence method of homogenization in periodic structures.