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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...

Conservative forms of Boltzmann's collision operator: Landau revisited

Cédric Villani (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We show that Boltzmann's collision operator can be written explicitly in divergence and double divergence forms. These conservative formulations may be of interest for both theoretical and numerical purposes. We give an application to the asymptotics of grazing collisions.

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