Displaying similar documents to “From classical mechanics to kinetic theory and fluid dynamics”

A Langevin Description for Driven Granular Gases

P. Maynar, M. I. García de Soria (2011)

Mathematical Modelling of Natural Phenomena

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The study of the fluctuations in the steady state of a heated granular system is reviewed. A Boltzmann-Langevin description can be built requiring consistency with the equations for the one- and two-particle correlation functions. From the Boltzmann-Langevin equation, Langevin equations for the total energy and the transverse velocity field are derived. The existence of a fluctuation-dissipation relation for the transverse velocity field...

The Boltzmann Equation: Mathematics and Applications

Carlo Cercignani (2007)

Bollettino dell'Unione Matematica Italiana

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The paper is subdivided into two parts. The first presents a recent result by the author concerning the existence of the solution of the Boltzmann equation for Maxwell molecules, without any cutoff in the collision kernel, when the solution depends on just one variable. At variance with the well-known theorem of DiPerna- Lions, conservation of energy is also shown to hold. The second part will concern rarefied gas dynamics problems, governed by the Boltzmann equation and con- cerning...

Computational fluctuating fluid dynamics

John B. Bell, Alejandro L. Garcia, Sarah A. Williams (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper describes the extension of a recently developed numerical solver for the Landau-Lifshitz Navier-Stokes (LLNS) equations to binary mixtures in three dimensions. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by using white-noise fluxes. These stochastic PDEs are more complicated in three dimensions due to the tensorial form of the correlations for the stochastic fluxes and in mixtures due to couplings of energy and concentration fluxes (, Soret...