This thesis consists of two papers devoted to the asymptotic analysis of eigenvalue problems in perforated domains. The first paper investigates by means of the two-scale convergence method the asymptotic behavior of eigenvalues and eigenfunctions of Stekloff eigenvalue problems in perforated domains. We prove a concise and precise homogenization result including convergence of gradients of eig...

We report on some recent progress in the mathematical theory of nonlinear fluid transport and poro-mechanics, specifically, the design, analysis and application of mathematical models for the flow of fluids driven by the coupled pressure and stress distributions within a deforming heterogeneous porous structure. The goal of this work is to develop a set of mathematical models of coupled flow an...

In this paper we discuss some numerical procedures involved in dynamic data driven simulations (DDDAS). The main objective of this paper is the recovery of the initial data as well as the media properties based on dynamic data. We consider the contaminant transport in porous media with a number of sensors placed at some locations. Based on measured data we propose to recover the permeability fi...

The stability analysis of Marangoni convection in porous media with a deformable upper free surface is investigated. The linear stability theory and the normal mode analysis are applied and the resulting eigenvalue problem is solved exactly. The Darcy law and the Brinkman model are used to describe the flow in the porous medium heated from below. The effect of the Crispation number, Bond number...

The stability analysis of Marangoni convection in porous media with a deformable upper free surface is investigated. The linear stability theory and the normal mode analysis are applied and the resulting eigenvalue problem is solved exactly. The Darcy law and the Brinkman model are used to describe the flow in the porous medium heated from below. The effect of the Crispation number, Bond number...

In this work, total smooth air-water interfacial areas were measured for a series of nine natural and model sandy porous media as a function of water saturation using synchrotron X-ray microtomography. Interfacial areas decreased linearly with water satuation, while the estimated maximum interfacial area compared favorably to the media geometric surface areas. Importantly, relative interfacial ...

Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure with prede®ned stati...

Using large scale computer simulations and pore network models of porous rock, we investigate the e€ect of correlated heterogeneity on two-phase ̄ow through porous media. First, we review and discuss the experimental evidence for correlated heterogeneity. We then employ the invasion percolation model of two-phase ̄ow in porous media to study the e€ect of correlated heterogeneity on rate-control...

in this paper, the effect of the brownian term in natural convection of cuo-water nanofluid inside a partially filled porous cavity, with internal heat generation has been studied. it is assumed that the viscosity and thermal conductivity of nanofluid consists of a static part and a brownian part of which is a function of temperature and the volume fraction of nanofluid. because of internal hea...