相关论文: Darcy's Law for Porous Media with Multiple Microst…

We present an experimental study of immiscible, two-phase fluid flow through a three-dimensional porous medium consisting of randomly-packed, monodisperse glass spheres. Our experiments combine refractive-index matching and laser-induced…

This paper presents a rigorous derivation of an effective model for fluid flow through a thin elastic porous membrane separating two fluid bulk domains. The microscopic setting involves a periodically structured porous membrane composed of…

Porous membranes are thin solid structures that allow the flow to pass through their tiny openings, called pores. Flow inertia may play a significant role in several filtration flows of natural and engineering interest. Here, we develop a…

In this paper, we investigate the global existence and uniqueness of strong solutions to 2D incompressible inhomogeneous Navier-Stokes equations with viscous coefficient depending on the density and with initial density being discontinuous…

In this paper we introduce and analyze, for two and three dimensions, a finite element method to approximate the natural frequencies of a flow system governed by the Stokes-Brinkman equations. Here, the fluid presents the capability of…

Large-scale electrical and thermal currents in ordinary metals are well approximated by effective medium theory: global transport properties are governed by the solution to homogenized coupled diffusion equations. In some metals, including…

Explicit analytical expressions for the drag and diffusion coefficients of a spherical particle attached to the interface between two immiscible fluids are constructed for the case of a small viscosity ratio between the fluid phases. The…

Single fluid porous medium systems are typically modeled at an averaged length scale termed the macroscale using Darcy's law. Standard approaches for modeling macroscale single fluid phase flow of non-Newtonian fluids extend Darcy's law,…

In many applications, one wants to model physical systems consisting of two different physical processes in two different domains that are coupled across a common interface. A crucial challenge is then that the solutions of the two…

Darcy's law and the Brinkman equation are two main models used for creeping fluid flows inside moving permeable particles. For these two models, the time derivative and the nonlinear convective terms of fluid velocity are neglected in the…

Equations governing the flow of a polar fluid, with pressure-dependent Newtonian viscosity, through a variable-porosity medium are developed. Averaged equations are obtained using intrinsic volume averaging. A drag function is introduced to…

In this note, we consider the homogenization of the compressible Navier-Stokes equations in a periodically perforated domain in $\mathbb{R}^3$. Assuming that the particle size scales like $\varepsilon^3$, where $\varepsilon>0$ is their…

Stokes flows with near-touching rigid particles induce near-singular lubrication forces under relative motion, making their accurate numerical treatment challenging. With the aim of controlling the accuracy with a computationally cheap…

In this work, we investigate the fundamental physical mechanism of the transition from Darcy to inertial (Darcy-Forchheimer) regime in steady-state flows through porous media, with the focus on vortex formation. We investigate their…

In this paper we investigate the interaction of fluid flow with a thin porous elastic layer. We consider two fluid-filled bulk domains which are separated by a thin periodically perforated layer consisting of a fluid and an elastic solid…

The accurate description of fluid flow and transport in fractured porous media is of paramount importance to capture the macroscopic behaviour of an oil reservoir, a geothermal system, or a CO2 sequestration site, to name few applications.…

We present a finite-difference scheme which solves the Stokes problem in the presence of curvilinear non-conforming interfaces and provides second-order accuracy on physical field (velocity, vorticity) and especially on pressure. The gist…

The three-dimensional jump conditions for the pressure and velocity fields, up to the second normal derivative,across an incompressible/inextensible interface in the Stokes regime are derived herein. The fluid viscosity is only piecewise…

We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel variational…

We address the discretization of two-phase Darcy flows in a fractured and deformable porous medium, including frictional contact between the matrix-fracture interfaces. Fractures are described as a network of planar surfaces leading to the…