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Hydrodynamic Regimes, Knudsen Layer, Numerical Schemes: Definition of Boundary Fluxes

Published online by Cambridge University Press:  03 June 2015

Christophe Besse ,
Saja Borghol ,
Thierry Goudon ,
Ingrid Lacroix-Violet  and
Jean-Paul Dudon
Christophe Besse*
Affiliation:
Project-Team SIMPAF, INRIA Lille Nord Europe Research Center, Park Plazza, 40 av. Halley, 59650 Villeneuve d’Ascq France Labo P. Painlevé UMR 8524 CNRS-Université des Sciences et Technologies Lille
Saja Borghol*
Affiliation:
Project-Team SIMPAF, INRIA Lille Nord Europe Research Center, Park Plazza, 40 av. Halley, 59650 Villeneuve d’Ascq France Labo P. Painlevé UMR 8524 CNRS-Université des Sciences et Technologies Lille
Thierry Goudon*
Affiliation:
Project-Team SIMPAF, INRIA Lille Nord Europe Research Center, Park Plazza, 40 av. Halley, 59650 Villeneuve d’Ascq France Labo P. Painlevé UMR 8524 CNRS-Université des Sciences et Technologies Lille
Ingrid Lacroix-Violet*
Affiliation:
Project-Team SIMPAF, INRIA Lille Nord Europe Research Center, Park Plazza, 40 av. Halley, 59650 Villeneuve d’Ascq France Labo P. Painlevé UMR 8524 CNRS-Université des Sciences et Technologies Lille
Jean-Paul Dudon*
Affiliation:
Thales Alenia Space, Cannes La Bocca
*
URL: http://math.univ-lille1.fr/∼goudon/ Email: christophe.besse@math.univ-lille1.fr
Email: saja.borghol@math.univ-lille1.fr
Corresponding author. Email: thierry.goudon@inria.fr
Email: ingrid.violet@math.univ-lille1.fr
Email: jean-paul.dudon@thalesaleniaspace.com
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Abstract

We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime. The typical example we discuss is the derivation of the Euler system from the BGK equation. The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.

Keywords

35L6535Q3582C8082C4076M1265M08Hydrodynamic regimesKnudsen layerfinite volume schemeinitial-boundary value problems for conservation lawsEvaporation-condensation problem
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 5 , October 2011 , pp. 519 - 561
Copyright
Copyright © Global-Science Press 2011

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