Abstract The onset of natural convection in a fluid-saturated anisotropic porous layer, which rotates about the vertical axis, under hypothesis local thermal non-equilibrium, is analysed. Since porosity medium assumed to be high, more suitable Darcy-Brinkman model adopted. Linear instability analysis conduction solution carried out. Nonlinear stability with respect $$L^2$$ <mml:math xmlns:mml="...

We prove that the signed porous medium equation can be regarded as limit of an optimal transport variational scheme, therefore extending the classical result for positive solutions of [13] and showing that an optimal transport approach is suited even for treating signed densities.

where τb = κρH is the optical depth of individual clumps or blobs, withH = l/f the “porosity length” for clumps of scale l and volume filling factor f . Note that optically thin blobs (τb ≪ 1) recover the non-porous limit, κeff → κ, whereas the limit of optically thick blobs (τb ≫ 1) has an effective opacity given by the ratio of their area l to mass mb(= l ρ/f = lρH), i.e. κeff → 1/ρH. The eff...

This work extends Perron’s method for the porous medium equation in the slow diffusion case. The main result shows that nonnegative continuous boundary functions are resolutive in a general cylindrical domain.

Flow through a saturated, granular, porous medium can lead to internal erosion, preferential flow enhancement, and the formation of channels within the bulk of the medium. We examine this phenomenon using a combination of experimental observations, continuum theory and numerical simulations in a minimal setting. Our experiments are carried out by forcing water through a Hele-Shaw cell packed wi...

Hydraulic fracturing is a phenomenon in which cracks propagate through the porous medium due to high pore fluid pressure. Hydraulic fracturing appears in different engineering disciplines either as a destructive phenomenon or as a useful technique. Modeling of this phenomenon in isothermal condition requires analysis of soil deformation, crack and pore fluid pressure interactions. In this paper...

A new formulation for shape and topology optimization in a Stokes flow is introduced. The investigated problem minimizes the total potential power of the flow. By combining a porous medium and a phase field approach we obtain a well-posed problem in a diffuse interface setting that can be reformulated into a problem without state equations. We can derive a sharp interface problem with zero perm...