Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions

作者：Caflisch Russel E^*; Lombardo Maria Carmela; Sammartino Marco

来源：Journal of Statistical Physics, 2011, 143(4): 725-739.

DOI：10.1007/s10955-011-0204-0

• Nonlocal boundary conditions
• Boltzmann equation
• Fluid dynamic limit

In this paper nonlocal boundary conditions for the Navier-Stokes equations are derived, starting from the Boltzmann equation in the limit for the Knudsen number being vanishingly small. In the same spirit of (Lombardo et al. in J. Stat. Phys. 130:69-82, 2008) where a nonlocal Poisson scattering kernel was introduced, a gaussian scattering kernel which models nonlocal interactions between the gas molecules and the wall boundary is proposed. It is proved to satisfy the global mass conservation and a generalized reciprocity relation. The asymptotic expansion of the boundary-value problem for the Boltzmann equation, provides, in the continuum limit, the Navier-Stokes equations associated with a class of nonlocal boundary conditions of the type used in turbulence modeling.

• 出版日期2011-5