Stochastic homogenization of multicontinuum heterogeneous flows

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:374

Article

Bessaih, Hakima¹  Maris, Razvan Florian² 

[1] Univ Wyoming, Dept Math & Stat, Dept 3036,1000 East Univ Ave, Laramie, WY 82071 USA

[2] Alexandru Loan Cuza Univ Iasi, Fac Econ & Business Adm, Bd Carol I 22, Iasi 700505, Romania

关键词: Multicontinuum;    Averaging;    Homogenization;    Invariant measures;    Porous media;   

DOI  :  10.1016/j.cam.2020.112746

来源: Elsevier

【 摘 要 】

We consider a multicontinuum model in porous media applications, which is described as a system of coupled flow equations. The coupling between different continua depends on many factors and its modeling is important for porous media applications. The coefficients depend on particle deposition that is described in terms of a stochastic process solution of an SDE. The stochastic process is considered to be faster than the flow motion and we introduce time-space scales to model the problem. Our goal is to pass to the limit in time and space and to find an associated averaged system. This is an averaging-homogenization problem, where the averages are computed in terms of the invariant measure associated to the fast motion and the spatial variable. We use the techniques developed in our previous paper, Bessaih et al. (2019) to model the interactions between the continua and derive the averaged model problem that can be used in many applications. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free