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

作者：Mathiaud J^*; Mieussens L

来源：Journal of Statistical Physics, 2016, 162(2): 397-414.

DOI：10.1007/s10955-015-1404-9

• Fokker-Planck model
• Ellipsoidal-statistical model
• H-theorem
• 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 can be obtained.

• 出版日期2016-1
• 单位中国地震局; INRIA