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On bounds of the drag for Stokes flow around a body without thickness

Didier Bresch — 1997

Commentationes Mathematicae Universitatis Carolinae

This paper is devoted to lower and upper bounds of the hydrodynamical drag T for a body in a Stokes flow. We obtain the upper bound since the solution for a flow in an annulus and therefore the hydrodynamical drag can be explicitly derived. The lower bound is obtained by comparison to the Newtonian capacity of a set and with the help of a result due to J. Simon [ 10 ] . The chosen approach provides an interesting lower bound which is independent of the interior of the body.

Operator-splitting and Lagrange multiplier domain decomposition methods for numerical simulation of two coupled Navier-Stokes fluids

Didier BreschJonas Koko — 2006

International Journal of Applied Mathematics and Computer Science

We present a numerical simulation of two coupled Navier-Stokes flows, using ope-rator-split-ting and optimization-based non-overlapping domain decomposition methods. The model problem consists of two Navier-Stokes fluids coupled, through a common interface, by a nonlinear transmission condition. Numerical experiments are carried out with two coupled fluids; one with an initial linear profile and the other in rest. As expected, the transmission condition generates a recirculation within the fluid...

Sur la théorie globale des équations de Navier-Stokes compressible

Didier BreschBenoît Desjardins — 2006

Journées Équations aux dérivées partielles

Le but de cet article est de présenter quelques résultats mathématiques plus ou moins récents sur la théorie de l’existence globale en temps (solutions faibles et solutions fortes) pour les équations de Navier-Stokes compressibles en dimension supérieure ou égale à deux sans aucune hypothèse de symétrie sur le domaine et sans aucune hypothèse sur la taille des données initiales.

Two shallow-water type models for viscoelastic flows from kinetic theory for polymers solutions

Gladys Narbona-ReinaDidier Bresch — 2013

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

In this work, depending on the relation between the Deborah, the Reynolds and the aspect ratio numbers, we formally derived shallow-water type systems starting from a micro-macro description for non-Newtonian fluids in a thin domain governed by an elastic dumbbell type model with a slip boundary condition at the bottom. The result has been announced by the authors in [G. Narbona-Reina, D. Bresch, Springer Verlag (2010)] and in the present paper, we provide a self-contained description, complete...

An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit

Didier BreschMarguerite GisclonChi-Kun Lin — 2005

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

The purpose of this work is to study an example of low Mach (Froude) number limit of compressible flows when the initial density (height) is almost equal to a function depending on x . This allows us to connect the viscous shallow water equation and the viscous lake equations. More precisely, we study this asymptotic with well prepared data in a periodic domain looking at the influence of the variability of the depth. The result concerns weak solutions. In a second part, we discuss the general low...

An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit

Didier BreschMarguerite GisclonChi-Kun Lin — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

The purpose of this work is to study an example of low Mach (Froude) number limit of compressible flows when the initial density (height) is almost equal to a function depending on . This allows us to connect the viscous shallow water equation and the viscous lake equations. More precisely, we study this asymptotic with well prepared data in a periodic domain looking at the influence of the variability of the depth. The result concerns weak solutions. In a second part, we discuss the...

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