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Homogenization of the transport equation describing convection-diffusion processes in a material with fine periodic structure

Šilhánek, David, Beneš, Michal (2023)

Programs and Algorithms of Numerical Mathematics

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...

Non-parallel plane Rayleigh Benard convection in cylindrical geometry

A. Golbabai (1995)

Applicationes Mathematicae

This paper considers the effect of a perturbed wall in regard to the classical Benard convection problem in which the lower rigid surface is of the form z = ε 2 g ( s ) , s=ε r, in axisymmetric cylindrical polar coordinates (r,ϕ,z). The boundary conditions at s=0 for the linear amplitude equation are found and it is shown that these conditions are different from those which apply to the nonlinear problem investigated by Brown and Stewartson [1], representing the distribution of convection cells near the center....

Stimuli-Responsive Polymers in Nanotechnology: Deposition and Possible Effect on Drug Release

A. L. Yarin (2008)

Mathematical Modelling of Natural Phenomena

Stimuli-responsive polymers result in on-demand regulation of properties and functioning of various nanoscale systems. In particular, they allow stimuli-responsive control of flow rates through membranes and nanofluidic devices with submicron channel sizes. They also allow regulation of drug release from nanoparticles and nanofibers in response to temperature or pH variation in the surrounding medium. In the present work two relevant mathematical models are introduced to address precipitation-driven...

Transport of pollutant in shallow water : a two time steps kinetic method

Emmanuel Audusse, Marie-Odile Bristeau (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The aim of this paper is to present a finite volume kinetic method to compute the transport of a passive pollutant by a flow modeled by the shallow water equations using a new time discretization that allows large time steps for the pollutant computation. For the hydrodynamic part the kinetic solver ensures – even in the case of a non flat bottom – the preservation of the steady state of a lake at rest, the non-negativity of the water height and the existence of an entropy inequality. On an other...

Transport of Pollutant in Shallow Water A Two Time Steps Kinetic Method

Emmanuel Audusse, Marie-Odile Bristeau (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to present a finite volume kinetic method to compute the transport of a passive pollutant by a flow modeled by the shallow water equations using a new time discretization that allows large time steps for the pollutant computation. For the hydrodynamic part the kinetic solver ensures – even in the case of a non flat bottom – the preservation of the steady state of a lake at rest, the non-negativity of the water height and the existence of an entropy inequality. On an other...

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