Homogenization in chemical reactive flows.
Homogenization in elastodynamics with force term depending on time.
Homogenization in perforated domains with rapidly pulsing perforations
The aim of this paper is to study a class of domains whose geometry strongly depends on time namely. More precisely, we consider parabolic equations in perforated domains with rapidly pulsing (in time) periodic perforations, with a homogeneous Neumann condition on the boundary of the holes. We study the asymptotic behavior of the solutions as the period of the holes goes to zero. Since standard conservation laws do not hold in this model, a first difficulty is to get a priori estimates of the...
Homogenization in perforated domains with rapidly pulsing perforations
The aim of this paper is to study a class of domains whose geometry strongly depends on time namely. More precisely, we consider parabolic equations in perforated domains with rapidly pulsing (in time) periodic perforations, with a homogeneous Neumann condition on the boundary of the holes. We study the asymptotic behavior of the solutions as the period ε of the holes goes to zero. Since standard conservation laws do not hold in this model, a first difficulty is to get a priori estimates...
Homogenization of a capillary phenomena.
We study the height of a liquid in a tube when it contains a great number of thin vertical bars and when its border is finely strained. For this, one uses an epi-convergence method.
Homogenization of a dual-permeability problem in two-component media with imperfect contact
In this paper, we study the macroscopic modeling of a steady fluid flow in an -periodic medium consisting of two interacting systems: fissures and blocks, with permeabilities of different order of magnitude and with the presence of flow barrier formulation at the interfacial contact. The homogenization procedure is performed by means of the two-scale convergence technique and it is shown that the macroscopic model is a one-pressure field model in a one-phase flow homogenized medium.
Homogenization of a one-dimensional model for compressible miscible flow in porous media
We discuss the homogenization of a one-dimensional model problem describing the motion of a compressible miscible flow in porous media. The flow is governed by a nonlinear system of parabolic type coupling the pressure and the concentration. Using the technique of renormalized solutions for parabolic equations and a compensated compactness argument, we prove the stability of the homogenization process.
Homogenization of a three-phase composites of double-porosity type
In this work we consider a diffusion problem in a periodic composite having three phases: matrix, fibers and interphase. The heat conductivities of the medium vary periodically with a period of size ( and ) in the transverse directions of the fibers. In addition, we assume that the conductivity of the interphase material and the anisotropy contrast of the material in the fibers are of the same order (the so-called double-porosity type scaling) while the matrix material has a conductivity of...
Homogenization of free boundary oscillations of an inviscid fluid in a porous reservoir
Homogenization of -laplacian in perforated domain
Homogenization of the compressible Navier–Stokes equations in a porous medium
We study the homogenization of the compressible Navier–Stokes system in a periodic porous medium (of period ) with Dirichlet boundary conditions. At the limit, we recover different systems depending on the scaling we take. In particular, we rigorously derive the so-called “porous medium equation”.
Homogenization of the compressible Navier–Stokes equations in a porous medium
We study the homogenization of the compressible Navier–Stokes system in a periodic porous medium (of period ε) with Dirichlet boundary conditions. At the limit, we recover different systems depending on the scaling we take. In particular, we rigorously derive the so-called “porous medium equation”.
Homogenization of the Stokes system in a thin film flow with rapidly varying thickness
Homogenization of the transport equation describing convection-diffusion processes in a material with fine periodic structure
In the present contribution we discuss mathematical homogenization and numerical solution of the elliptic problem describing convection-diffusion processes in a material with fine periodic structure. Transport processes such as heat conduction or transport of contaminants through porous media are typically associated with convection-diffusion equations. It is well known that the application of the classical Galerkin finite element method is inappropriate in this case since the discrete solution...
Homogenized double porosity models for poro-elastic media with interfacial flow barrier
In the paper a Barenblatt-Biot consolidation model for flows in periodic porous elastic media is derived by means of the two-scale convergence technique. Starting with the fluid flow of a slightly compressible viscous fluid through a two-component poro-elastic medium separated by a periodic interfacial barrier, described by the Biot model of consolidation with the Deresiewicz-Skalak interface boundary condition and assuming that the period is too small compared with the size of the medium, the limiting...
Homogenized model for flow in partially fractured media.
Homogenized models for a short-time filtration in elastic porous media.
HOT-pressing process modeling for medium density fiberboard (MDF).
Hybrid central-upwind schemes for numerical resolution of two-phase flows
In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which...
Hybrid central-upwind schemes for numerical resolution of two-phase flows
In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the Jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which...