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Central-Upwind Schemes for the Saint-Venant System

Alexander Kurganov, Doron Levy (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present one- and two-dimensional central-upwind schemes for approximating solutions of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant system has steady-state solutions in which nonzero flux gradients are exactly balanced by the source terms. It is a challenging problem to preserve this delicate balance with numerical schemes. Small perturbations of these states are also very difficult to compute. Our approach is based on extending semi-discrete central...

Characterization of collision kernels

Laurent Desvillettes, Francesco Salvarani (2003)

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

In this paper we show how abstract physical requirements are enough to characterize the classical collision kernels appearing in kinetic equations. In particular Boltzmann and Landau kernels are derived.

Characterization of collision kernels

Laurent Desvillettes, Francesco Salvarani (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we show how abstract physical requirements are enough to characterize the classical collision kernels appearing in kinetic equations. In particular Boltzmann and Landau kernels are derived.

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.

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