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Displaying 121 –
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357
We derive a posteriori error estimates for singularly
perturbed reaction–diffusion problems which yield a guaranteed
upper bound on the discretization error and are fully and easily
computable. Moreover, they are also locally efficient and robust in
the sense that they represent local lower bounds for the actual
error, up to a generic constant independent in particular of the
reaction coefficient. We present our results in the framework of
the vertex-centered finite volume method but their nature...
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.
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.
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...
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”.
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”.
Propagation of polymerization fronts with liquid monomer and liquid polymer is considered
and the influence of vibrations on critical conditions of convective instability is
studied. The model includes the heat equation, the equation for the concentration and the
Navier-Stokes equations considered under the Boussinesq approximation. Linear stability
analysis of the problem is fulfilled, and the convective instability boundary is found
depending on...
The aim of this paper is to study the effect of vibrations on convective instability of
reaction fronts in porous media. The model contains reaction-diffusion equations coupled
with the Darcy equation. Linear stability analysis is carried out and the convective
instability boundary is found. The results are compared with direct numerical
simulations.
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