A Generalized Finite Volume Method for Density Driven Flows in Porous Media

Adaptivity in the Finite Volume Discretization of Variable Density Flows in Porous Media

Finite volume hydromechanical simulation in porous media

Cell-centered finite volume methods are prevailing in numerical simulation of flow in porous media. However, due to the lack of cell-centered finite volume methods for mechanics, coupled flow and deformation is usually treated either by coupled finite-volume-finite element discretizations, or within a finite element setting. The former approach is unfavorable as it introduces two separate grid ...

Combined Mixed Hybrid Finite Element and Finite Volume Method for Flow in Porous Media

This paper describes a numerical solution for two dimensional partial differential equations modeling (or arising from) a fluid flow and transport phenomena. The diffusion equation is discretized by the mixed hybrid finite element method. The saturation equation is solved by a finite volume method. We start with incompressible single-phase flow and move step-bystep to the black-oil model and co...

Finite volume scheme for two-phase flows in heterogeneous porous media involving capillary pressure discontinuities

We study a one-dimensional model for two-phase flows in heterogeneous media, in which the capillary pressure functions can be discontinuous with respect to space. We first give a model, leading to a system of degenerated nonlinear parabolic equations spatially coupled by nonlinear transmission conditions. We approximate the solution of our problem thanks to a monotonous finite volume scheme. Th...

Combined Nodal Method and Finite Volume Method for Flow in Porous Media

This paper describes a numerical solution for two dimensional partial differential equations modeling (or arising from) a fluid flow and transport phenomena. The diffusion equation is discretized by the Nodal methods. The saturation equation is solved by a finite volume method. We start with incompressible single-phase flow and move step-by-step to the black-oil model and compressible two phase...