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- Title
Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions.
- Authors
Caflisch, Russel E.; Lombardo, Maria Carmela; Sammartino, Marco
- Abstract
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, ) 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.
- Subjects
NAVIER-Stokes equations; POISSON summation formula; GAUSSIAN distribution; FREE molecular flow; MATHEMATICAL models of turbulence; RECIPROCITY theorems; MATHEMATICAL continuum
- Publication
Journal of Statistical Physics, 2011, Vol 143, Issue 4, p725
- ISSN
0022-4715
- Publication type
Article
- DOI
10.1007/s10955-011-0204-0