A stochastic multiscale framework for modeling flow through random heterogeneous porous media

A stochastic mixed finite element heterogeneous multiscale method for flow in porous media

A computational methodology is developed to efficiently perform uncertainty quantification for fluid transport in porous media in the presence of both stochastic permeability and multiple scales. In order to capture the small scale heterogeneity, a new mixed multiscale finite element method is developed within the framework of the heterogeneous multiscale method (HMM) in the spatial domain. Thi...

A stochastic heterogeneous multiscale method for porous media flow

A new multiscale algorithm is introduced based on the framework of the heterogeneous multiscale method. The mixed finite element method used ensures continuity of the flux within the entire domain. This method is shown to be free of “resonance error” and uses less memory than the mixed multiscale finite element method. To account for the highstochastic dimensionality of the permeability field, ...

Numerical Homogenization of Well Singularities in the Flow Transport through Heterogeneous Porous Media

Stochastic analysis of flow in a heterogeneous unsaturated-saturated system

[1] In this study we develop a stochastic model for transient unsaturated-saturated flow in randomly heterogeneous media with the method of moment equations. We first derive partial differential equations governing the statistical moments of the flow quantities by perturbation expansions and then implement these equations under general conditions with the method of finite differences. The stoch...

Adaptive Variational Multiscale Methods for Multiphase Flow in Porous Media

We aim in this paper to give a unified presentation to some important approaches in multi-phase flow in porous media within the framework of multiscale methods. Thereafter, we will present a modern outlook indicating future research directions in this field.