Related papers: Two-scale analysis of a non standard transmission …

Two-scale homogenization limits of parabolic cross-diffusion systems in a heterogeneous medium with no-flux boundary conditions are proved. The heterogeneity of the medium is reflected in the diffusion coefficients or by the perforated…

A finite element method with mass-lumping and flux upwinding, is formulated for solving the immiscible two-phase flow problem in porous media. The method approximates directly the wetting phase pressure and saturation, which are the primary…

We study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial differential equations appear in the modelization of…

The paper is devoted to the homogenization of porous piezoelectric materials saturated by electrically inert fluid. The solid part of a representative volume element consists of the piezoelectric skeleton with embedded conductors. The pore…

The paper addresses a two-temperature model for simulating compressible two-phase flow taking into account diffusion processes related to the heat conduction and viscosity of the phases. This model is reduced from the two-phase…

Close-contact melting refers to the process of a heat source melting its way into a phase-change material. Of special interest is the close-contact melting velocity, or more specifically the relative velocity between the heat source and the…

In this paper we present a fully-coupled, two-scale homogenization method for dynamic loading in the spirit of FE$^2$ methods. The framework considers the balance of linear momentum including inertia at the microscale to capture possible…

A cold, thin film of liquid impinging on an isothermal hot, horizontal surface has been investigated. An approximate solution for the velocity and temperature distributions in the flow along the horizontal surface is developed, which…

The paper presents a new type of weakly nonlinear two-scale model of controllable periodic porous piezoelectric structures saturated by Newtonian fluids. The flow is propelled by peristaltic deformation of microchannels which is induced due…

The problem of steady mixed convection boundary-layer flow on a cooled vertical permeable circular cylinder embedded in a fluid-saturated porous medium is studied. Here, we evaluate the flow and heat transfer characteristics numerically for…

We consider a model describing the steady flow of compressible heat-conducting chemically-reacting multi-component mixture. We show the existence of strong solutions under the additional assumption that the mixture is sufficiently dense. We…

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…

In many interfacial flow systems, variations of surface properties lead to novel and interesting behaviors. In this work a three-dimensional model of flow dynamics for multicomponent vesicles is presented. The surface composition is modeled…

The following paper presents two simulation strategies for compressible two-phase or multicomponent flows. One is a full non-equilibrium model in which the pressure and velocity are driven towards the equilibrium at interfaces by numerical…

A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…

The present paper deals with the homogenization of the heat conduction which takes place in a binary three-dimensional medium consisting of an ambiental phase having conductivity of unity order and a rectangular honeycomb structure formed…

A bio-heat transfer model for biological tissues in a micro-scale and periodical settings is investigated . It is assumed that the model is a two-component system consisting of solid particles representing tissue cells and interconnected…

We consider a non reactive multi component gas mixture.We propose a class of models, which can be easily generalized to multiple species. The two species mixture is modelled by a system of kinetic BGK equations featuring two interaction…

We study a one dimensional model for two-phase flows in heterogeneous media, in which the capillary pressure functions can be discontinuous with respect to space. We first give a model, leading to a system of degenerated non-linear…

In this work we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists on two fully coupled, non-linear equations: a degenerate parabolic equation and an elliptic equation. The proposed…