Julien Mathiaud

A Fokker-Planck Model of the Boltzmann Equation with Correct Prandtl Number

We propose an extension of the Fokker–Planck model of the Boltzmann equation to get a correct Prandtl number in the Compressible Navier–Stokes asymptotics. This is obtained by replacing the diffusion coefficient (which is the equilibrium temperature) by a non diagonal temperature tensor, like the Ellipsoidal-Statistical model is obtained from the Bathnagar–Gross–Krook model of the Boltzmann equation. Our model is proved to satisfy the properties of conservation and a H-theorem. A Chapman–Enskog analysis and two numerical tests show that a correct Prandtl number of

Some Aspects of the Asymptotics Leading from Gas-Particles Equations Towards Multiphase Flows Equations

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A Fokker–Planck Model of the Boltzmann Equation with Correct Prandtl Number for Polyatomic Gases

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Numerical boundary conditions in Finite Volume and Discontinuous Galerkin schemes for the simulation of rarefied flows along solid boundaries

The slip/jump coefficients and the Knudsen-layer functions for the time-dependent version of the generalized slip-flow theory have been obtained for the Ellipsoidal Statistical (ES) model up to the second order of the Knudsen number expansion. In particular, simple but exact conversion formulas between the ES and Bhatnagar–Gross–Krook (BGK) model have been established.