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Choosing Hydrodynamic Fields

J. W. Dufty, J. J. Brey (2011)

Mathematical Modelling of Natural Phenomena

Continuum mechanics (e.g., hydrodynamics, elasticity theory) is based on the assumption that a small set of fields provides a closed description on large space and time scales. Conditions governing the choice for these fields are discussed in the context of granular fluids and multi-component fluids. In the first case, the relevance of temperature or energy as a hydrodynamic field is justified. For mixtures, the use of a total temperature and single...

Chute stationnaire d’un solide dans un fluide visqueux incompressible au-dessus d’un plan incliné. Partie 2

M. Hillairet (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

Nous montrons dans cette étude l’existence de configurations stationnaires où une bille tombe le long d’un plan incliné sans le toucher. Nous donnons également des propriétés qualitatives de ces configurations. En particulier, nous nous intéressons à l’orientation du plan par rapport à la verticale quand la masse de la bille est proche de celle d’un volume équivalent de liquide i.e., quand l’écoulement autour de la bille est lent.

Classical solutions for the equations modelling the motion of a ball in a bidimensional incompressible perfect fluid

Jaime H. Ortega, Lionel Rosier, Takéo Takahashi (2005)

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

In this paper we investigate the motion of a rigid ball in an incompressible perfect fluid occupying 2 . We prove the global in time existence and the uniqueness of the classical solution for this fluid-structure problem. The proof relies mainly on weighted estimates for the vorticity associated with the strong solution of a fluid-structure problem obtained by incorporating some dissipation.

Classical solutions for the equations modelling the motion of a ball in a bidimensional incompressible perfect fluid

Jaime H. Ortega, Lionel Rosier, Takéo Takahashi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we investigate the motion of a rigid ball in an incompressible perfect fluid occupying 2 . We prove the global in time existence and the uniqueness of the classical solution for this fluid-structure problem. The proof relies mainly on weighted estimates for the vorticity associated with the strong solution of a fluid-structure problem obtained by incorporating some dissipation.

Combined finite element -- finite volume method (convergence analysis)

Mária Lukáčová-Medviďová (1997)

Commentationes Mathematicae Universitatis Carolinae

We present an efficient numerical method for solving viscous compressible fluid flows. The basic idea is to combine finite volume and finite element methods in an appropriate way. Thus nonlinear convective terms are discretized by the finite volume method over a finite volume mesh dual to a triangular grid. Diffusion terms are discretized by the conforming piecewise linear finite element method. In the paper we study theoretical properties of this scheme for the scalar nonlinear convection-diffusion...

Combustion in hydraulically resisted flows.

Gregory I. Sivashinsky (2007)

RACSAM

The effects of hydraulic resistance on premixed gas combustion in tubes and inert porous beds are discussed on the basis of recent research. It is found that the hydraulic resistance causes a gradual precompression and preheating of the unburned gas adjacent to the advancing deflagration which may lead (after an extended induction period) to a localized thermal explosion triggering an abrupt transition from deglagrative to detonative combustion. The hydraulic resistance has a profound effect also...

Comparaison entre modèles d'ondes de surface en dimension 2

Youcef Mammeri (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

Partant du principe de conservation de la masse et du principe fondamental de la dynamique, on retrouve l'équation d'Euler nous permettant de décrire les modèles asymptotiques de propagation d'ondes dans des eaux peu profondes en dimension 1. Pour décrire la propagation des ondes en dimension 2, Kadomtsev et Petviashvili [ 15 (1970) 539] utilisent une perturbation linéaire de l'équation de KdV. Mais cela ne précise pas si les équations ainsi obtenues dérivent de l'équation d'Euler, c'est ce que...

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