A Domain Decomposition Analysis for a Two-Scale Linear Transport Problem

François Golse; Shi Jin; C. David Levermore

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 6, page 869-892
  • ISSN: 0764-583X

Abstract

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We present a domain decomposition theory on an interface problem for 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 the diffusive region, the solution in the non-diffusive region is independent of the density in the diffusive region. However, the diffusive and the non-diffusive regions are coupled at the interface at the next order of approximation. In particular, our algorithm avoids iterating the diffusion and transport solutions as is done in most other methods — see for example Bal–Maday (2002). Our analysis is based instead on an accurate description of the boundary layer at the interface matching the phase-space density of particles leaving the non-diffusive region to the bulk density that solves the diffusion equation.

How to cite

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Golse, François, Jin, Shi, and David Levermore, C.. "A Domain Decomposition Analysis for a Two-Scale Linear Transport Problem." ESAIM: Mathematical Modelling and Numerical Analysis 37.6 (2010): 869-892. <http://eudml.org/doc/194196>.

@article{Golse2010,
abstract = { We present a domain decomposition theory on an interface problem for 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 the diffusive region, the solution in the non-diffusive region is independent of the density in the diffusive region. However, the diffusive and the non-diffusive regions are coupled at the interface at the next order of approximation. In particular, our algorithm avoids iterating the diffusion and transport solutions as is done in most other methods — see for example Bal–Maday (2002). Our analysis is based instead on an accurate description of the boundary layer at the interface matching the phase-space density of particles leaving the non-diffusive region to the bulk density that solves the diffusion equation. },
author = {Golse, François, Jin, Shi, David Levermore, C.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Domain decomposition; transport equation; diffusion approximation; kinetic-fluid coupling.; domain decomposition; kinetic-fluid coupling; interface problem; linear transport equation; algorithm; boundary layer},
language = {eng},
month = {3},
number = {6},
pages = {869-892},
publisher = {EDP Sciences},
title = {A Domain Decomposition Analysis for a Two-Scale Linear Transport Problem},
url = {http://eudml.org/doc/194196},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Golse, François
AU - Jin, Shi
AU - David Levermore, C.
TI - A Domain Decomposition Analysis for a Two-Scale Linear Transport Problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 6
SP - 869
EP - 892
AB - We present a domain decomposition theory on an interface problem for 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 the diffusive region, the solution in the non-diffusive region is independent of the density in the diffusive region. However, the diffusive and the non-diffusive regions are coupled at the interface at the next order of approximation. In particular, our algorithm avoids iterating the diffusion and transport solutions as is done in most other methods — see for example Bal–Maday (2002). Our analysis is based instead on an accurate description of the boundary layer at the interface matching the phase-space density of particles leaving the non-diffusive region to the bulk density that solves the diffusion equation.
LA - eng
KW - Domain decomposition; transport equation; diffusion approximation; kinetic-fluid coupling.; domain decomposition; kinetic-fluid coupling; interface problem; linear transport equation; algorithm; boundary layer
UR - http://eudml.org/doc/194196
ER -

References

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