# Hybrid Multiscale Finite Volume method for two-phase flow in porous media

### Details

Serval ID

serval:BIB_23E8754DE530

Type

**Article**: article from journal or magazin.

Collection

Publications

Fund

Title

Hybrid Multiscale Finite Volume method for two-phase flow in porous media

Journal

Journal of Computational Physics

ISSN-L

0021-9991

Publication state

Published

Issued date

2013

Peer-reviewed

Oui

Volume

250

Pages

293-307

Language

english

Notes

Tomin2013

Abstract

We present a novel hybrid (or multiphysics) algorithm, which couples

pore-scale and Darcy descriptions of two-phase flow in porous media.

The flow at the pore-scale is described by the Navier?Stokes equations,

and the Volume of Fluid (VOF) method is used to model the evolution

of the fluid?fluid interface. An extension of the Multiscale Finite

Volume (MsFV) method is employed to construct the Darcy-scale problem.

First, a set of local interpolators for pressure and velocity is

constructed by solving the Navier?Stokes equations; then, a coarse

mass-conservation problem is constructed by averaging the pore-scale

velocity over the cells of a coarse grid, which act as control volumes;

finally, a conservative pore-scale velocity field is reconstructed

and used to advect the fluid?fluid interface. The method relies on

the localization assumptions used to compute the interpolators (which

are quite straightforward extensions of the standard MsFV) and on

the postulate that the coarse-scale fluxes are proportional to the

coarse-pressure differences. By numerical simulations of two-phase

problems, we demonstrate that these assumptions provide hybrid solutions

that are in good agreement with reference pore-scale solutions and

are able to model the transition from stable to unstable flow regimes.

Our hybrid method can naturally take advantage of several adaptive

strategies and allows considering pore-scale fluxes only in some

regions, while Darcy fluxes are used in the rest of the domain. Moreover,

since the method relies on the assumption that the relationship between

coarse-scale fluxes and pressure differences is local, it can be

used as a numerical tool to investigate the limits of validity of

Darcy's law and to understand the link between pore-scale quantities

and their corresponding Darcy-scale variables.

pore-scale and Darcy descriptions of two-phase flow in porous media.

The flow at the pore-scale is described by the Navier?Stokes equations,

and the Volume of Fluid (VOF) method is used to model the evolution

of the fluid?fluid interface. An extension of the Multiscale Finite

Volume (MsFV) method is employed to construct the Darcy-scale problem.

First, a set of local interpolators for pressure and velocity is

constructed by solving the Navier?Stokes equations; then, a coarse

mass-conservation problem is constructed by averaging the pore-scale

velocity over the cells of a coarse grid, which act as control volumes;

finally, a conservative pore-scale velocity field is reconstructed

and used to advect the fluid?fluid interface. The method relies on

the localization assumptions used to compute the interpolators (which

are quite straightforward extensions of the standard MsFV) and on

the postulate that the coarse-scale fluxes are proportional to the

coarse-pressure differences. By numerical simulations of two-phase

problems, we demonstrate that these assumptions provide hybrid solutions

that are in good agreement with reference pore-scale solutions and

are able to model the transition from stable to unstable flow regimes.

Our hybrid method can naturally take advantage of several adaptive

strategies and allows considering pore-scale fluxes only in some

regions, while Darcy fluxes are used in the rest of the domain. Moreover,

since the method relies on the assumption that the relationship between

coarse-scale fluxes and pressure differences is local, it can be

used as a numerical tool to investigate the limits of validity of

Darcy's law and to understand the link between pore-scale quantities

and their corresponding Darcy-scale variables.

Create date

25/11/2013 15:33

Last modification date

18/11/2016 12:18