在雙孔隙隨機介質上單相流的橢圓方程問題

Abstract

考慮一個通過兩種不同物質所組成、高度異質性多孔隨機介質上的線性單向流。我們以橢圓方程來描述此現象。藉由2-scale converge in the mean 的方法獲得均質化問題。

Consider the linearized equations of slightly compressible single fluid flows through a highly heterogeneous random porous medium, consisting of two types of material. Due to the high heterogeneity of the two materials, the ratio of their permeability coefficients is of order ε2, whereεis the characteristic scale of heterogeneities. A homogenized problem is obtained by using the stochastic two scale convergence in the mean and by means of convergence results adapted to a priori estimates and to the random geometry.