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Homogenized models for filtration and for acoustic wave propagation in thermo-elastic porous media

Published online by Cambridge University Press:  01 June 2008

A. MEIRMANOV
A. MEIRMANOV*
Affiliation:
Belgorod State University, 308015 Belgorod, Russia email: meirmanov@bsu.edu.ru
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Abstract

A system of differential equations describing the joint motion of thermo-elastic porous body and slightly compressible viscous thermofluid occupying pore space is considered. Although the problem is correct in an appropriate functional space, it is very hard to tackle due to the fact that its main differential equations involve non-smooth oscillatory coefficients, both big and small, under the differentiation operators. 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 a result, we derive Biot's system of equations of thermo-poroelasticity, a similar system, consisting of anisotropic Lamé equations for a thermoelastic solid coupled with acoustic equations for a thermofluid, Darcy's system of filtration, or acoustic equations for a thermofluid, according to ratios between physical parameters. The proofs are based on Nguetseng's two-scale convergence method of homogenization in periodic structures.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 19 , Issue 3 , June 2008 , pp. 259 - 284
Copyright
Copyright © Cambridge University Press 2008

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