Eduard Marušić-Paloka

HOMOGENIZATION OF A NONLINEAR CONVECTION-DIFFUSION EQUATION WITH RAPIDLY OSCILLATING COEFFICIENTS AND STRONG CONVECTION

A Cauchy problem for a nonlinear convection-diffusion equation with periodic rapidly oscillating coefficients is studied. Under the assumption that the convection term is large, it is proved that the limit (homogenized) equation is a nonlinear diffusion equation which shows dispersion effects. The convergence of the homogenization procedure is justified by using a new version of a two-scale convergence technique adapted to rapidly moving coordinates.

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.

A HOMOGENIZED MODEL OF AN UNDERGROUND WASTE REPOSITORY INCLUDING A DISTURBED ZONE

The mathematical model describing the leaking of an underground waste repository should include the multiscale geometry and the large variation of the geological coefficients. Numerical simulations for performance assessments using such a local and detailed model are unrealistic, and there is a need to replace this local model (mesoscopic model) by a global one (macroscopic model). After introducing a small parameter

Modelling of heat transfer in a laminar flow through a helical pipe

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On the Stokes Paradox for Power-Law Fluids

, linking the relative size of the waste packages to the repository module size and to geological parameters, a first-order accurate macroscopic model of a repository module is obtained by studying the asymptotic behavior of the mesoscopic model when

NONLINEAR EFFECTS FOR FLOW IN PERIODICALLY CONSTRICTED CHANNEL CAUSED BY HIGH INJECTION RATE

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On reactive solute transport through a curved pipe

tends to 0. The mathematical homogenization method that we use herein leads to an accurate macroscopic model which could be used as a global repository model for far field numerical simulations in performance assessment.

Non-isothermal fluid flow through a thin pipe with cooling

We study the flow of a heat-conducting incompressible Newtonian fluid through a helical pipe with cooling. The pipes thickness and the helix step are considered as the small parameter @e. Using asymptotic analysis with respect to @e, we derive the simplified mathematical model describing the heat transfer through the pipe. The error estimate for the approximation is proved.

WEAK NONLINEAR CORRECTIONS FOR DARCY’S LAW

We study a purely viscous flow of a non-Newtonian fluid obeying the power-law in an exterior domain. We prove that for pseudo-plastic fluids the Stokes paradox does not take place, while for the dilatant fluids it takes place in any space dimension n if the flow index is larger or equal to n.

STEADY FLOW OF A NON-NEWTONIAN FLUID IN UNBOUNDED CHANNELS AND PIPES

We consider a stationary viscous incompressible flow through a periodically constricted channel with the period and thickness ∊, governed by a strong injection of order ∊-1. We prove the well-posedness of the homogenized problem and the convergence of the homogenization process. We obtain a nonlinear filtration law and we give the Taylor expansion of the filtration velocity as a function of the pressure gradient.