Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions

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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.
Lingua originaleEnglish
pagine (da-a)725-739
Numero di pagine15
RivistaJournal of Statistical Physics
Volume143(4)
Stato di pubblicazionePublished - 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

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cita questo

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title = "Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions",
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.",
keywords = "Nonlocal boundary conditions; Boltzmann equation; Fluid dynamic limit",
author = "Sammartino, {Marco Maria Luigi} and Lombardo, {Maria Carmela} and Caflisch, {Russel E.}",
year = "2011",
language = "English",
volume = "143(4)",
pages = "725--739",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",

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T1 - Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions

AU - Sammartino, Marco Maria Luigi

AU - Lombardo, Maria Carmela

AU - Caflisch, Russel E.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Nonlocal boundary conditions; Boltzmann equation; Fluid dynamic limit

UR - http://hdl.handle.net/10447/61191

M3 - Article

VL - 143(4)

SP - 725

EP - 739

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

ER -