Non-local scattering kernel and the hydrodynamic limit

Maria Carmela Lombardo; Russel E. Caflisch; Marco Sammartino

doi:10.1007/s10955-007-9360-7

Non-local scattering kernel and the hydrodynamic limit

Maria Carmela Lombardo, Russel E. Caflisch, Marco Sammartino

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	69-82
Number of pages	14
Journal	Journal of Statistical Physics
Volume	130
Issue number	1
DOIs	https://doi.org/10.1007/s10955-007-9360-7
State	Published - Jan 2008

Keywords

Boltzmann equation
Hydrodynamic limit
Navier-Stokes flow
Nonlocal boundary conditions

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-007-9360-7

Cite this

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title = "Non-local scattering kernel and the hydrodynamic limit",

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.",

keywords = "Boltzmann equation, Hydrodynamic limit, Navier-Stokes flow, Nonlocal boundary conditions",

author = "Lombardo, {Maria Carmela} and Caflisch, {Russel E.} and Marco Sammartino",

note = "Funding Information: Acknowledgements The work of the authors (M.C.L.) and (M.S.) was supported by the INDAM, under the 2005-2007 PRIN grant “Nonlinear Propagation and Stability in Thermodynamical Processes of Continuous Media”. They also thank C. Cercignani and A. Majorana for the enlightening discussions on the topics of this paper.",

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AU - Caflisch, Russel E.

AU - Sammartino, Marco

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N2 - 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.

AB - 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.

KW - Boltzmann equation

KW - Hydrodynamic limit

KW - Navier-Stokes flow

KW - Nonlocal boundary conditions

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SP - 69

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

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Non-local scattering kernel and the hydrodynamic limit

Abstract

Keywords

ASJC Scopus subject areas

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