In this paper, we consider the Cauchy problem for a porous medium equation in Fingero-imbibition phenomena arising in double phase flow through porous media during oil recovery process. Fingero-imbibition is a physical phenomenon which represents the simultaneous occurrence of two special phenomenon viz. fingering and imbibitions in a porous media. We obtain a series solution of porous medium e...

The enactment of strict laws on reducing pollution and controlling combustion has given rise to the necessity of considering a new approach to energy supply in the future. One such approach is the use of hydrogen as an alternative to fossil fuels. Hydrogen and synthesis gas are typically produced through the partial oxidation of methane in porous media. This process was theoretically simula...

We use Stokesian Dynamics simulations to study the microscopic motion of particles suspended in fluids passing through porous media. We construct model porous media with fixed spherical particles, and allow mobile ones to move through this fixed bed under the action of an ambient velocity field. We first consider the pore scale motion of individual suspended particles at pore junctions. The rel...

In the focusing problem, we study solutions to the porous medium equation ∂tu = (u) whose initial distributions are positive in the exterior of a compact 2D region and zero inside. We assume that the initial interface is elongated (i.e., has an aspect ratio > 1), and possesses reflectional symmetry with respect to both the xand y-axes. We implement a numerical scheme that adapts the numerical g...

Many flows observed in subsurface rock formations are unsaturated flows through a medium containing fractures. In cases where the fracture voids are small and nonconnective, one finds that little flow occurs within those voids. Under these conditions, the fractures act as barriers which impede background flow in the underlying matrix. From a computational point of view, discrete modeling of the...

This paper deals with the mathematical modeling of the coupled flow/deformation problem characterizing the industrial production of a composite material by injection moulding. The role of inertia, typically non–negligible during a short early time, is studied in terms of models of reduced complexity. Using the theory of characteristics and some considerations on the energy of the system we are ...