Related papers: A Multiscale Model of Partial Melts 1: Effective E…
In a companion paper, equations for partially molten media were derived using two-scale homogenization theory. One advantage of homogenization is that material properties, such as permeability and viscosity, readily emerge. A caveat is that…
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…
The paper deals with the homogenization of deformable porous media saturated by two-component electrolytes. The model relevant to the microscopic scale describes steady states of the medium while reflecting essential physical phenomena,…
We prove the two-scale transformation method which allows rigorous homogenisation of problems defined on locally periodic domains by transformation on periodic domains. The idea to consider periodic substitute problems was originally…
This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential…
The paper addresses the homogenization of a micro-model of poroelasticity coupled with thermal effects for two-constituent media and with imperfect interfacial contact.The homogenized model is obtained by means of the two-scale convergence…
We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in an earlier paper by two-scale…
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…
It is shown that the equilibrium Generalized Mean Spherical Model of fluid structure may be extended to nonequilibrium states with equation of state information used in equilibrium replaced by an exact condition on the two-body distribution…
In this paper we employ homogenization techniques to provide a rigorous derivation of the Darcy scale model for precipitation and dissolution in porous media proposed in [19]. The starting point is the pore scale model in [12], which is a…
The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…
A phase-field model for two-phase immiscible, incompressible porous media flow with surface tension effects is considered. The pore-scale model consists of a strongly coupled system of Stokes-Cahn-Hilliard equations. The fluids are…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
We are investigating the effective heat transfer in complex systems involving porous media and surrounding fluid layers in the context of mathematical homogenization. We differentiate between two fundamentally different cases: Case (a),…
In this short paper, periodic homogenization of a steady heat flow in two-component media with highly adhesive contact is performed via the two-scale convergence technique. Our micro-model is based on mass conservation for the heat flow in…
The paper deals with homogenization of a model problem describing an immiscible compressible two-phase flow in random statistically homogeneous porous media. We derive the effective (macroscopic) problem and prove the convergence of…
In this work, we contribute to the broader understanding of inverse problems by introducing a versatile multiscale modeling framework tailored to the challenges of sediment concentration estimation. Specifically, we propose a novel approach…
The notion of periodic two-scale convergence and the method of periodic unfolding are prominent and useful tools in multiscale modeling and analysis of PDEs with rapidly oscillating periodic coefficients. In this paper we are interested in…
We investigated the effective influence of grain structures on the heat transfer between a fluid and solid domain using mathematical homogenization. The presented model consists of heat equations inside the different domains, coupled…
An overview of some recent developments in inhomogeneous models is presented. As the volume and precision of cosmological data improves, it will become more and more essential to understand the non-linear behaviour of the Einstein field…