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

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 for polyatomic gases. This is obtained by replacing the diffusion coefficient (which is the equilibrium temperature) by a non diagonal temperatur...

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Bibliographic Details
Published in:Journal of statistical physics 2017-09, Vol.168 (5), p.1031-1055
Main Authors: Mathiaud, J., Mieussens, L.
Format: Article
Language:English
Subjects:
Analysis of PDEs
Boltzmann transport equation
Compressibility
Computational fluid dynamics
Diffusion coefficient
Energy conservation
Fluid flow
Fluid mechanics
Internal energy
Mathematical and Computational Physics
Mathematical models
Mathematics
Mechanics
Navier-Stokes equations
Physical Chemistry
Physics
Physics and Astronomy
Polyatomic gases
Prandtl number
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Thermal energy
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Summary: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 for polyatomic gases. 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, and by adding a diffusion term for the internal energy. Our model is proved to satisfy the properties of conservation and a H-theorem. A Chapman–Enskog analysis shows how to compute the transport coefficients of our model. Some numerical tests are performed to illustrate that a correct Prandtl number can be obtained.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-017-1837-4