Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions |
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Authors: | Email author" target="_blank">Russel?E?CaflischEmail author Maria?Carmela?Lombardo Marco?Sammartino |
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Institution: | 1.Department of Mathematics,UCLA,Los Angeles,USA;2.Dipartimento di Matematica,Università di Palermo,Palermo,Italy |
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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. |
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Keywords: | |
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