Related papers: The Darcy problem with porosity depending exponent…
A linear system of differential equations describing a joint motion of a thermoelastic porous body with a sufficiently large Lame's constants (absolutelty rigid body) and a thermofluid, occupying porous space, is considered. The rigorous…
We provide a rigorous mathematical study of an asymptotic model describing Darcy flow with free boundary in a low amplitude/large wavelength approximation. In particular, we prove several well-posedness results in critical spaces.…
We study the flow of a micropolar fluid in a thin domain with microstructure, i.e. a thin domain with thickness $\varepsilon$ which is perforated by periodically distributed solid cylinders of size $a_\varepsilon$. A main feature of this…
We consider the inverse problem of determining the permeability from the pressure in a Darcy model of flow in a porous medium. Mathematically the problem is to find the diffusion coefficient for a linear uniformly elliptic partial…
This paper is concerned with Darcy's law for an incompressible viscous fluid flowing in a porous medium. We establish the sharp $O(\sqrt{\e})$ convergence rate in a periodically perforated and bounded domain in $R^d$ for $d\ge 2$, where…
In porous media, there are three known regimes of fluid flows, namely, pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are usually treated separately in literature. To study complex flows when all three regimes…
In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous medium governed by Darcy's law. We show formation of singularities with infinite energy and for finite energy we obtain…
We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore…
In this article we investigate the permeability of a porous medium as given in Darcy's law. The permeability is described by an effective hydraulic pore radius in the porous medium, the fluctuation in local hydraulic pore radii, the length…
Fluid infiltration of a permeable brick in contact with a pressurized reservoir of fluid is considered. A stochastic model, informed by Darcy's law and the incompressibility of the fluid, shows how the heterogeneity of the permeability…
We study the existence of solutions for Darcy's problem coupled with the heat equation under singular forcing; the right-hand side of the heat equation corresponds to a Dirac measure. The studied model allows thermal diffusion and viscosity…
In the present paper, we study the existence, uniqueness and behaviour in time of the solutions to the Darcy-B\'enard problem for an extended-quasi-thermal-incompressible fluid-saturated porous medium uniformly heated from below. Unlike the…
Slow flow of a single fluid through a porous medium is well understood on a macroscopic level through Darcy's law, a linear relation between flow rate and a combination of pressure differences, viscosity, and gravitational forces. Two-phase…
Fractured porous media or double porosity media are common in nature. At the same time, accurate modeling remains a significant challenge due to bi-modal pore size distribution, anisotropy, multi-field coupling, and various flow patterns.…
Perfectly incompressible materials do not exist in nature but are a useful approximation of several media which can be deformed in non-isothermal processes but undergo very small volume variation. In this paper the linear analysis of the…
It is shown that the problem of moisture propagation in porous media with a nonlinear relation between the mass flux and the pressure gradient as a counterpart of the Darcy law exhibits the property of bounded speed of propagation even in…
The problem of diffusion in a porous medium with a spatially varying porosity is considered. The particular microstructure analyzed comprises a collection of impenetrable spheres, though the methods developed are general. Two different…
We introduce a Darcy-scale model to describe compressible multi-component flow in a fully saturated porous medium. In order to capture cross-diffusive effects between the different species correctly, we make use of the Maxwell--Stefan…
Hysteresis in the relation between the capillary pressure and the moisture content in unsaturated porous media, which is due to surface tension at the liquid-gas interface, exhibits strong degeneracy in the resulting mass balance equation.…
The flow of incompressible fluids through porous media plays a crucial role in many technological applications such as enhanced oil recovery and geological carbon-dioxide sequestration. The flow within numerous natural and synthetic porous…