Related papers: A Multiscale Model of Partial Melts 2: Numerical R…
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…
In this work, a two-dimensional time-fractional subdiffusion model is developed to investigate the underlying transport phenomena evolving in a binary medium comprised of two sub-domains occupied by homogeneous material. We utilise an…
For many materials, macroscopic mechanical behavior is determined by an intricate microstructure. Understanding the relation between these two scales helps scientists and engineers design better materials. The relation which maps…
This paper is devoted to the homogenization of weakly coupled cooperative parabolic systems in strong convection regime with purely periodic coefficients. Our approach is to factor out oscillations from the solution via principal…
A linear system of differential equations describing a joint motion of thermoelastic porous body and thermofluid occupying porous space is considered. Although the problem is linear, it is very hard to tackle due to the fact that its main…
We consider the homogenization of a model of reactive flows through periodic porous media involving a single solute which can be absorbed and desorbed on the pore boundaries. This is a system of two convection-diffusion equations, one in…
In this paper we present the two-level homogenization of the flow in a deformable double-porous structure described at two characteristic scales. The higher level porosity associated with the mesoscopic structure is constituted by channels…
We aim at understanding transport in porous materials including regions with both high and low diffusivities. For such scenarios, the transport becomes structured (here: {\em micro-macro}). The geometry we have in mind includes regions of…
Variational-hemivariational inequalities are an important mathematical framework for nonsmooth problems. The framework can be used to study application problems from physical sciences and engineering that involve non-smooth and even…
We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance…
A linear system of differential equations describing a joint motion of elastic porous body and fluid occupying porous space is considered. Although the problem is linear, it is very hard to tackle due to the fact that its main differential…
We consider the problem of homogenizing the Maxwell equations for periodic composites. The analysis is based on Bloch-Floquet theory. We calculate explicitly the reflection coefficient for a half-space, and derive and implement a…
In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the convergence of the iteration scheme of this algorithm and the…
In this paper, we discuss a general framework for multicontinuum homogenization. Multicontinuum models are widely used in many applications and some derivations for these models are established. In these models, several macroscopic…
In this work, we review and analyze both the theoretical and numerical aspects of strongly and weakly coupled thermoelastic systems. By employing spectral analysis techniques and establishing uniform resolvent estimates, we derive uniform…
The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture.…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly…
Double porosity models for the liquid filtration in an absolutely rigid body is derived from homogenization theory. The governing equations of the fluid dynamics on the microscopic level consist of the Stokes system for a slightly…
The inhomogeneous Muskat problem models the dynamics of an interface between two fluids of differing characteristics inside a non-uniform porous medium. We consider the case of a porous media with a permeability jump across a horizontal…