This paper is concerned with the homogenization of model problems in periodic porous media when important phenomena occur on the boundaries of the pores. To this end, we generalize the notion of two-scale convergence for sequences of functions which are deened on periodic surfaces. We apply our results to two model problems : the rst one is a diiusion equation in a porous medium with a Fourier ...

A novel numerical method is presented for the simulation of flow in porous media, based on a mesoscopic-scale modelling using smoothed particle hydrodynamics. The method is demonstrated to provide encouraging results for both saturated and unsaturated porous media flow. The Darcy law is confirmed for low drift velocities in a saturated medium, while nonlinear behaviour is observed for higher va...

Abstract An innovative and groundbreaking mathematical approach is proposed for the determination of the properties of reservoir materials, when oil reserves together with water are moving through porous media. Such problem seems to be very important for oil reservoir engineering. So, the above problem is reduced to the solution of a non-linear singular integral equation, which is numerically e...

in the present paper, an analysis was carried out to investigate effects of radiation on a free convection flow bounded by a vertical surface embedded in a porous medium with constant suction velocity. it was under the influence of uniform magnetic field in the presence of a homogenous chemical reaction and viscous dissipation with constant heat and mass flux. the non-dimensional governing equa...

Abstract We establish Hölder continuity for locally bounded weak solutions to certain parabolic systems of porous medium type, i.e. $$\begin{aligned} \partial _t \mathbf{u}-\mathrm{div}(m|\mathbf{u}|^{m-1}D\mathbf{u})=0,\quad m&gt;0. \end{aligned}$$ ∂ t</mml:...

&lt;p style='text-indent:20px;'&gt;We study a porous medium equation with dissipative and hyperdiffusive effects no sign restrictions on the diffusion coefficient.&lt;/p&gt;