MATHIAUD, Julien; MIEUSSENS, Luc

doi:10.1007/s10955-015-1404-9

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MATHIAUD, Julien
Centre d'études scientifiques et techniques d'Aquitaine (CESTA-CEA) [CESTA]
Institut de Mathématiques de Bordeaux [IMB]

MIEUSSENS, Luc
Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
Institut de Mathématiques de Bordeaux [IMB]

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Journal of Statistical Physics. 2016, vol. 162, n° 2, p. 397-414

Springer Verlag

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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 (ES) is obtained from the Bathnagar-Gross-Krook model (BGK) 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 2/3 can be obtained.< Leer menos

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H-theorem

Prandtl number

Fokker-Planck model

Ellipsoidal-Statistical model

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A Fokker-Planck model of the Boltzmann equation with correct Prandtl number

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