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A Domain Decomposition Analysisfor a Two-Scale Linear Transport Problem

Published online by Cambridge University Press:  15 November 2003

François Golse ,
Shi Jin  and
C. David Levermore
François Golse
Affiliation:
Institut Universitaire de France, Département de Mathématiques et Applications, École Normale Supérieure Paris, 45 rue d'Ulm, 75230 Paris Cedex 05, France. golse@dma.ens.fr.
Shi Jin
Affiliation:
Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA. jin@math.wisc.edu.
C. David Levermore
Affiliation:
Department of Mathematics, Institute of Physical Sciences and Technology, University of Maryland, College Park, Maryland 20742, USA. lvrmr@math.umd.edu.
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Abstract

We present a domain decomposition theory on an interface problemfor the linear transport equation between a diffusive and a non-diffusive region.To leading order, i.e. up to an error of the order of the mean free path in thediffusive region, the solution in the non-diffusive region is independent of thedensity in the diffusive region. However, the diffusive and the non-diffusive regionsare coupled at the interface at the next order of approximation. In particular, ouralgorithm avoids iterating the diffusion and transport solutions as is done in mostother methods — see for example Bal–Maday (2002). Our analysis is based instead on an accurate description of the boundarylayer at the interface matching the phase-space density of particles leaving thenon-diffusive region to the bulk density that solves the diffusion equation.

Keywords

Domain decompositiontransport equationdiffusion approximationkinetic-fluid coupling.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 6 , November 2003 , pp. 869 - 892
Copyright
© EDP Sciences, SMAI, 2003

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