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 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;

In this work a glass micromodel which its grains and pores are non-uniform in size, shape and distribution is considered as porous medium. A two-dimensional random network model of micromodel with non-uniform pores has been constructed. The non-uniformity of porous model is achieved by assigning parametric distribution functions to pores throat and pores length, which was measured using ima...

Understanding the transport properties of a porous medium from a knowledge of its microstructure is a problem of great interest in the physical, chemical, and biological sciences. Using a first-passage time method, we compute the mean survival time tau of a Brownian particle among perfectly absorbing traps for a wide class of triply periodic porous media, including minimal surfaces. We find tha...

Constant flux atom deposition into a porous medium is shown to generate a dense overlayer and a diffusion profile. Scaling analysis shows that the overlayer acts as a dynamic control for atomic diffusion in the porous substrate. This is modeled by generalizing the porous diffusion equation with a time-dependent diffusion coefficient equivalent to a nonlinear rescaling of time.