English
Related papers

Related papers: Darcy's Law for Porous Media with Multiple Microst…

200 papers

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…

Analysis of PDEs · Mathematics 2025-08-07 Markus Gahn , Maria Neuss-Radu

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…

Analysis of PDEs · Mathematics 2017-12-12 Marius Paicu , Ping Zhang

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…

Numerical Analysis · Mathematics 2025-07-14 Felipe Lepe , Gonzalo Rivera , Jesus Vellojin

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…

Analysis of PDEs · Mathematics 2021-02-03 Guillaume Bal , Andrew Lucas , Mitchell Luskin

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…

Soft Condensed Matter · Physics 2016-04-20 Aaron Dörr , Steffen Hardt

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,…

Fluid Dynamics · Physics 2019-11-26 Christopher A. Bowers , Cass T. Miller

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…

Numerical Analysis · Mathematics 2020-01-17 Karl Erik Holter , Miroslav Kuchta , Kent-Andre Mardal

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…

Computational Physics · Physics 2015-02-10 Liang Wang , Lian-Ping Wang , Zhaoli Guo , Jianchun Mi

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…

Fluid Dynamics · Physics 2025-12-04 M. H. Hamdan , D. C. Roach

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…

Analysis of PDEs · Mathematics 2022-11-28 Peter Bella , Florian Oschmann

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…

Numerical Analysis · Mathematics 2024-11-26 Anna Broms , Alex H. Barnett , Anna-Karin Tornberg

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…

Fluid Dynamics · Physics 2025-11-18 Dawid Strzelczyk , Gregor Kosec , Maciej Matyka

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…

Analysis of PDEs · Mathematics 2021-12-08 Markus Gahn , Maria Neuss-Radu , Willi Jäger

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.…

Numerical Analysis · Mathematics 2019-08-01 Alessio Fumagalli , Eirik Keilegavlen

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…

Fluid Dynamics · Physics 2011-10-07 Abdelkader Hammouti , Anaël Lemaître

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…

Fluid Dynamics · Physics 2013-09-09 Prerna Gera , David Salac

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…

Numerical Analysis · Mathematics 2015-06-02 John W. Barrett , Harald Garcke , Robert Nürnberg

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…

Numerical Analysis · Mathematics 2022-01-24 Francesco Bonaldi , Jérôme Droniou , Roland Masson , Antoine Pasteau