We shall describe the derivation of homogenized equations (in an asymp- totics of mean-field type) for systems consisting of a cloud of particles dispersed in a material enclosed in a bounded domain. We shall consider in particular the homoge- nization of the Stokes problem leading to the Brinkman force and the homogenization of a model describing the heat exchange between the material and the dispersed phase leading to a (time-dependent) two-temperature equation. In both cases, the homogenized equations can be rigorously derived using similar form for the correctors.
Ricci, V. (2012). Homogenization of equations describing materials interacting with clouds of particles. In Book of abstract 7th European Conference on Elliptic and Parabolic Problems.
Homogenization of equations describing materials interacting with clouds of particles
RICCI, Valeria
2012-01-01
Abstract
We shall describe the derivation of homogenized equations (in an asymp- totics of mean-field type) for systems consisting of a cloud of particles dispersed in a material enclosed in a bounded domain. We shall consider in particular the homoge- nization of the Stokes problem leading to the Brinkman force and the homogenization of a model describing the heat exchange between the material and the dispersed phase leading to a (time-dependent) two-temperature equation. In both cases, the homogenized equations can be rigorously derived using similar form for the correctors.
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