Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions

Russel 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 2011

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Rarefied Gas
Nonlocal Boundary Conditions
rarefied gases
Boltzmann Equation
Asymptotic Analysis
Navier-Stokes equation
Navier-Stokes Equations
Scattering
boundary conditions
kernel
Turbulence Modeling
Nonlocal Interactions
Knudsen number
Knudsen flow
Mass Conservation
Continuum Limit
Reciprocity
scattering
boundary value problems
Asymptotic Expansion

Keywords

  • Boltzmann equation
  • Fluid dynamic limit
  • Nonlocal boundary conditions

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions. / Caflisch, Russel; Lombardo, Maria Carmela; Sammartino, Marco.

In: Journal of Statistical Physics, Vol. 143, No. 4, 05.2011, p. 725-739.

Research output: Contribution to journalArticle

Caflisch, Russel ; Lombardo, Maria Carmela ; Sammartino, Marco. / Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions. In: Journal of Statistical Physics. 2011 ; Vol. 143, No. 4. pp. 725-739.
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