TY - JOUR
T1 - Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions
AU - Caflisch, Russel E.
AU - Lombardo, Maria Carmela
AU - Sammartino, Marco
N1 - Funding Information:
Acknowledgements The work of the second (MCL) and third (MS) author has been partially supported by INDAM and the Dept of Mathematics of Palermo through the grant “Fondi di potenziamento della ricerca.”
PY - 2011/5
Y1 - 2011/5
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 - Boltzmann equation
KW - Fluid dynamic limit
KW - Nonlocal boundary conditions
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U2 - 10.1007/s10955-011-0204-0
DO - 10.1007/s10955-011-0204-0
M3 - Article
AN - SCOPUS:79956208963
SN - 0022-4715
VL - 143
SP - 725
EP - 739
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 4
ER -