Sanja Marušić

Comparison between Darcy and Brinkman laws in a fracture

Different laws are used for modeling flows in porous media. In this paper, we focus on Brinkman and Darcy law. We derive them from microscopic equations by upscaling, compare them and estimate the error made by their application. Our results justify the use of Brinkman law.

Decay of a fluid flow in a weakly permeable domain

We prove the exponential decay of the velocity and the pressure for a fluid flow in a weakly permeable domain Ω e (e.g. narrow channel). The value of the velocity is prescribed on some portion of the boundary S e such that it has a zero normal flux on each connex part of S e .

Écoulement non newtonien à travers un filtre mince

Resume On considere l’injection d’un fluide non newtonien a travers une paroi mince (d’epaisseur O (e)) perforee periodiquement (de periode e). A partir de l’ecoulement microscopique decrit par le systeme de Stokes incompressible a viscosite non lineaire (loi de Carreau) et en etudiant le comportement asymptotique lorsque e → 0, on obtient la loi caracterisant l’ecoulement global.

Computation of the permeability tensor for the fluid flow through a periodic net of thin channels

We consider the local problem obtained by the homogenization of the Stokes and Navier-Stokes equations in a periodic porous medium consisting of many thin channels. By taking the limit as thickness of the channels goes to zero we obtain the explicit formula for the permeability tensor.

Analysis of the Reynolds Equation for Lubrication in Case of Pressure-Dependent Viscosity

We study the Reynolds equation, describing the ow of a lubricant, in case of pressure-dependent viscosity. First we prove the existence and uniqueness of the solution. Then, we study the asymptotic behavior of the solution in case of periodic roughness via homogenization method. Some interesting nonlocal effects appear due to the nonlinearity.

An asymptotic expansion for the Neumann sieve problem

In this paper, we study the Neumann sieve problem for the Laplace equation. Our objective is to compute the complete asymptotic expansion for the problem. The expansion consists of the interior part, in the vicinity of the filter, and an exterior part, far away from the filter. The interior approximation is a Bakhvalov-Panasenko-type expansion with terms defined by a sequence of auxiliary problems on infinite stripes and matching with the exterior expansion. We prove the related error estimate.

Asymptotic behaviour of sharp Sobolev constants in thin domains

In this paper we study the asymptotic behaviour of the constants in Sobolev inequalities in thin domains with respect to the thickness of the domain e. We prove that the sharp Sobolev constants in thin domains converge to the sharp Sobolev constant on the lower-dimensional domain, as e tends to zero.

Nonlinear reynolds equation for lubrication of a rapidly rotating shaft

Using the homogenization theory, we derive the nonlinear Reynolds equation governing the process of lubrication of a slipper bearing with rapidly rotating shaft. We prove that this nonliner lubrication law is an approximation of the full Navier-Stokes equations in a thin cylinder with periodic roughness. The analyticity of the nonlinear function giving the relation between the velocity and the pressure drop is proved. The first term in its Taylors expansion is the classical linear Reynolds law. Boundary layer correctors are computed.