Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions

Russel E. Caflisch, Maria Carmela Lombardo, Marco Sammartino

Research output: Contribution to journalArticle

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, 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.

Original languageEnglish (US)
Pages (from-to)725-739
Number of pages15
JournalJournal of Statistical Physics
Volume143
Issue number4
DOIs
StatePublished - May 1 2011

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Keywords

  • Boltzmann equation
  • Fluid dynamic limit
  • Nonlocal boundary conditions

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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