Mixed GMsFEM for linear poroelasticity problems in heterogeneous porous media

Hybrid Mixed Discretization Methods for Combustion Problems in Porous Media

This paper presents numerical methods for the simulation of combustion processes in porous media. The equations governing the ow in the porous medium are discretized by the mixed nite element method on Raviart{Thomas elements of lowest order. Hybridization is applied to transform the resulting equations into a form more convenient for the solution by multigrid methods. Special emphasis is put o...

Linear Poroelasticity

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...

Multilevel Upscaling in Heterogeneous Porous Media

The multiscale structure of heterogeneous porous media prevents a straightforward numerical treatment of the underlying mathematical ow models. In particular, fully resolved ow simulations are intractable and yet the ne-scale structure of a porous medium may signiicantly innuence the coarse-scale properties of the solution (e.g., average ow rates). Consequently, homogenization or upscaling proc...

Transient Fluid Flow in Heterogeneous Porous Media

A stable Alternating Direction Implicit finite-difference algorithm is used to model transient fiuid flow in heterogeneous porous media. In connection with the laboratory system for pressure transient testing of core permeability, the effects of permeability heterogeneities on the characteristics of the pressure transient were investigated. The results show that the early portion of the pressur...