In this article, we develop a set of partial differential equations describing the flow of a dusty fluid in variable porosity media. The developed equations take into account the effect of the porous microstructure on the flowing phases. We presented and overview of the equations governing the flow of a dusty gas in various type media, including that in naturally occurring porous media. Numeric...

An interconnected set of algorithms is presented for the simulation of two-phase ow in porous media achieving more than two orders of magnitudes acceleration. The accuracy and e ciency of the approach is demonstrated through 2D and 3D numerical experiments for a range of two-phase porous media problems involving single cracks, heterogeneous permeability, and hydrophobic and hydrophilic media

An Algebraic Multiscale Solver (AMS) for the pressure system of equations arising from incompressible flow in heterogeneous porous media is developed. The algorithm allows for several independent preconditioning stages to deal with the full spectrum of errors. In addition to the fine-scale system of equations, AMS requires information about the superimposed (dual) coarse grid, which is used for...

A large number of multiscale finite-volume methods have been developed over the past decade to compute conservative approximations to multiphase flow problems in heterogeneous porous media. In particular, several iterative and algebraic multiscale frameworks that seek to reduce the fine-scale residual towards machine precision have been presented. Common for all such methods is that they rely o...

A new model for turbulent flows in porous media is developed. The spatialand time fluctuations in this new model are tied together and treated as a single quantity. This novel treatment of the fluctuations leads to a natural construction of the k and e type equations for rigid and isotropic porous media in which all the kinetic energy filtered in the averaging process is modeled. The same terms...

In this paper we discuss the formulation of the governing equations that describe ow of uids in porous media Various types of uid ow ranging from single phase ow to compositional ow are considered It is shown that all the di erential equations governing these types of ow can be e ectively rewritten in a fractional ow formulation i e in terms of a global pressure and saturation or saturations an...

A mesoscopic numerical tool has been developed in this study for predictions of the effective thermal conductivities for microscale random porous media. To solve the energy transport equation with complex multiphase porous geometries, a lattice Boltzmann algorithm has been introduced to tackle the conjugate heat transfer among different phases. With boundary conditions correctly chosen, the alg...

∗ In this chapter we uncover through numerical simulation the velocity and pressure fields inside a model porous medium composed of an infinitely extending array of staggered square rods. These microtransport simulations allow for the prediction of macrotransport parameters that are of value to the volume-averaged description of fluid motion in porous media. We focus on computing the macroscopi...