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A discrete kinetic approximation for the incompressible Navier-Stokes equations

Maria Francesca Carfora, Roberto Natalini (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we introduce a new class of numerical schemes for the incompressible Navier-Stokes equations, which are inspired by the theory of discrete kinetic schemes for compressible fluids. For these approximations it is possible to give a stability condition, based on a discrete velocities version of the Boltzmann H-theorem. Numerical tests are performed to investigate their convergence and accuracy.

A geometric lower bound on Grad’s number

Alessio Figalli (2009)

ESAIM: Control, Optimisation and Calculus of Variations

In this note we provide a new geometric lower bound on the so-called Grad’s number of a domain Ø in terms of how far Ø is from being axisymmetric. Such an estimate is important in the study of the trend to equilibrium for the Boltzmann equation for dilute gases.

A geometric lower bound on Grad's number

Alessio Figalli (2008)

ESAIM: Control, Optimisation and Calculus of Variations

In this note we provide a new geometric lower bound on the so-called Grad's number of a domain Ω in terms of how far Ω is from being axisymmetric. Such an estimate is important in the study of the trend to equilibrium for the Boltzmann equation for dilute gases.

A Langevin Description for Driven Granular Gases

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

Mathematical Modelling of Natural Phenomena

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 is also...

Around 3D Boltzmann non linear operator without angular cutoff, a new formulation

Radjesvarane Alexandre (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose a new formulation of the 3D Boltzmann non linear operator, without assuming Grad's angular cutoff hypothesis, and for intermolecular laws behaving as 1/rs, with s> 2. It involves natural pseudo differential operators, under a form which is analogous to the Landau operator. It may be used in the study of the associated equations, and more precisely in the non homogeneous framework.

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