Stochastic homogenization and macroscopic modelling of composites and flow through porous media

Abstract

The aim of this contribution is mainly twofold. First, the stochastic two-scale convergence in the mean developed by Bourgeat et al. [13] is used to derive the macroscopic models of: (i) diffusion in random porous medium, (ii) nonstationary flow of Stokesian fluid through random linear elastic porous medium. Second, the multi-scale convergence method developed by Allaire and Briane [7] for the case of several microperiodic scales is extended to random distribution of heterogeneities characterized by separated scales (stochastic reiterated homogenization). .Svrha ovog rada je uglavnom dvostruka. Prvo, stohasticka dvoskalna konvergencija u srednjem razvijena od Bourgeat i saradnika [13] se koristi za izvodjenje sledecih makroskopskih modela: (i) difuzije u slucajnoj poroznoj sredini, (ii) nenstacionarno tecenje Stokes-ovog fluda kroz slucajnu linearno elasticnu poroznu sredinu. Drugo, metoda viseskalne konvergencije razvijena od Allaire-a i Briane-a [7] za slucaj vise mikroperiodicnih skala je ovde prosiren na slucajni raspored heterogenosti okarakterisan razdvojenim skalama (stohasticka homogenizacija sa reiteracijom). .