6533b860fe1ef96bd12c3b76

RESEARCH PRODUCT

Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions

Russel E. CaflischMarco SammartinoMaria Carmela Lombardo

subject

Nonlocal boundary conditionGaussianMathematical analysisTurbulence modelingStatistical and Nonlinear PhysicsMixed boundary conditionPoisson distributionBoltzmann equationPhysics::Fluid DynamicsBoltzmann equationFluid dynamic limitsymbols.namesakesymbolsKnudsen numberAsymptotic expansionConservation of massSettore MAT/07 - Fisica MatematicaMathematical PhysicsMathematics

description

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.

yearjournalcountryeditionlanguage
2011-04-30
10.1007/s10955-011-0204-0http://hdl.handle.net/10447/61191