Non-local scattering kernel and the hydrodynamic limit

Maria Carmela Lombardo, Russel Caflisch, Marco Sammartino

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)69-82
Number of pages14
JournalJournal of Statistical Physics
Volume130
Issue number1
DOIs
StatePublished - Jan 2008

Fingerprint

Hydrodynamic Limit
hydrodynamics
Scattering
kernel
scattering
Fluid
Nonlocal Boundary Conditions
Mass Conservation
fluids
Reciprocity
Kinetic Theory
conservation laws
kinetic theory
Navier-Stokes equation
Conservation Laws
Navier-Stokes Equations
Molecules
boundary conditions
Interaction
molecules

Keywords

  • Boltzmann equation
  • Hydrodynamic limit
  • Navier-Stokes flow
  • Nonlocal boundary conditions

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Non-local scattering kernel and the hydrodynamic limit. / Lombardo, Maria Carmela; Caflisch, Russel; Sammartino, Marco.

In: Journal of Statistical Physics, Vol. 130, No. 1, 01.2008, p. 69-82.

Research output: Contribution to journalArticle

Lombardo, Maria Carmela ; Caflisch, Russel ; Sammartino, Marco. / Non-local scattering kernel and the hydrodynamic limit. In: Journal of Statistical Physics. 2008 ; Vol. 130, No. 1. pp. 69-82.
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