6533b871fe1ef96bd12d1ba0

RESEARCH PRODUCT

Non-Local Scattering Kernel and the Hydrodynamic Limit

Russel E. CaflischMaria Carmela LombardoMarco Sammartino

subject

GeneralizationMathematical analysisStatistical and Nonlinear PhysicsKnudsen layerStokes flowBoltzmann equationPhysics::Fluid Dynamicssymbols.namesakeNonlocal boundary conditions Fluid dynamic limit Navier-Stokes Boltzmann equationsClassical mechanicsStokes' lawKinetic theory of gasessymbolsLimit (mathematics)Conservation of massMathematical PhysicsMathematics

description

In this paper we study the interaction of a fluid with a wall in the framework of the kinetic theory. We consider the possibility that the fluid molecules can penetrate the wall to be reflected by the inner layers of the wall. This results in a scattering kernel which is a non-local generalization of the classical Maxwell scattering kernel. The proposed scattering kernel satisfies a global mass conservation law and a generalized reciprocity relation. We study the hydrodynamic limit performing a Knudsen layer analysis, and derive a new class of (weakly) nonlocal boundary conditions to be imposed to the Navier-Stokes equations.

yearjournalcountryeditionlanguage
2007-10-03Journal of Statistical Physics
https://doi.org/10.1007/s10955-007-9360-7