Related papers: POREMAPS: A finite difference based Porous Media A…
We study a new fully averaged poroelastic Kirchhoff plate model coupled with the flow of an incompressible, viscous fluid governed by the time-dependent Stokes equations. The fully averaged formulation offers several advantages over the…
We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media. Some of the methods developed using the framework are already known…
Anisotropic light transport is extremely common among scattering materials, yet a comprehensive picture of how macroscopic diffusion is determined by microscopic tensor scattering coefficients is not fully established yet. In this work, we…
This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…
Microtomography is a powerful method of materials investigation. It enables to obtain physical properties of porous media non-destructively that is useful in studies. One of the application ways is a calculation of porosity, pore sizes,…
We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule…
In this article, two novel numerical methods have been developed for simulating fluid/porous particle interactions in three-dimensional (3D) Stokes flow. The Brinkman-Debye-Bueche model is adopted for the fluid flow inside the porous…
Stochastic modeling has become a popular approach to quantify uncertainty in flows through heterogeneous porous media. The uncertainty in heterogeneous structure properties is often parameterized by a high-dimensional random variable. This…
Fiber-reinforced soft biological tissues are typically modeled as hyperelastic, anisotropic, and nearly incompressible materials. To enforce incompressibility a multiplicative split of the deformation gradient into a volumetric and an…
Biot's theory provides a framework for computing seismic wavefields in fluid saturated porous media. Here we implement a velocity-stress staggered grid 2D finite difference algorithm to model the wave-propagation in poroelastic media. The…
We propose finite element methods for compressible barotropic Stokes systems. We state convergence results for these methods and outline their proofs. The principal tools of the proofs are higher integrability estimates for the discrete…
An open-sourced multiphase Darcy-Brinkman approach is proposed to simulate two-phase flow in hybrid systems containing both solid-free regions and porous matrices. This micro-continuum model is rooted in elementary physics and volume…
The micro-continuum method is a novel approach to simulate flow and transport in multiscale porous materials. For such materials, the domain can be divided into three sub-domains depending on the local porosity {\epsilon}: fully resolved…
The surface texture of materials plays a critical role in wettability, turbulence and transport phenomena. In order to design surfaces for these applications, it is desirable to characterise non-smooth and porous materials by their ability…
When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…
We model incompressible flows with an adaptive stabilized finite element method Stokes flows, which solves a discretely stable saddle-point problem to approximate the velocity-pressure pair. Additionally, this saddle-point problem delivers…
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…
Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…
In the last decades, significant progress has been made in understanding the multiphase displacement through porous media with homogeneous wettability and its relation to the pore geometry. However, the role of wettability at the scale of…
Anisotropic Porous Medium Equation (APME) is developed as an extension of the Porous Medium Equation (PME) for anisotropic porous media. A special analytical solution is derived for APME for time-independent diffusion. Anisotropic mesh…