Diffusion Limit of the Lorentz Model: Asymptotic Preserving Schemes

Christophe Buet; Stéphane Cordier; Brigitte Lucquin-Desreux; Simona Mancini

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 36, Issue: 4, page 631-655
  • ISSN: 0764-583X

Abstract

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This paper deals with the diffusion limit of a kinetic equation where the collisions are modeled by a Lorentz type operator. The main aim is to construct a discrete scheme to approximate this equation which gives for any value of the Knudsen number, and in particular at the diffusive limit, the right discrete diffusion equation with the same value of the diffusion coefficient as in the continuous case. We are also naturally interested with a discretization which can be used with few velocity discretization points, in order to reduce the cost of computation.

How to cite

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Buet, Christophe, et al. "Diffusion Limit of the Lorentz Model: Asymptotic Preserving Schemes." ESAIM: Mathematical Modelling and Numerical Analysis 36.4 (2010): 631-655. <http://eudml.org/doc/194119>.

@article{Buet2010,
abstract = { This paper deals with the diffusion limit of a kinetic equation where the collisions are modeled by a Lorentz type operator. The main aim is to construct a discrete scheme to approximate this equation which gives for any value of the Knudsen number, and in particular at the diffusive limit, the right discrete diffusion equation with the same value of the diffusion coefficient as in the continuous case. We are also naturally interested with a discretization which can be used with few velocity discretization points, in order to reduce the cost of computation. },
author = {Buet, Christophe, Cordier, Stéphane, Lucquin-Desreux, Brigitte, Mancini, Simona},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Hilbert expansion; diffusion limit.; diffusion limit},
language = {eng},
month = {3},
number = {4},
pages = {631-655},
publisher = {EDP Sciences},
title = {Diffusion Limit of the Lorentz Model: Asymptotic Preserving Schemes},
url = {http://eudml.org/doc/194119},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Buet, Christophe
AU - Cordier, Stéphane
AU - Lucquin-Desreux, Brigitte
AU - Mancini, Simona
TI - Diffusion Limit of the Lorentz Model: Asymptotic Preserving Schemes
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 4
SP - 631
EP - 655
AB - This paper deals with the diffusion limit of a kinetic equation where the collisions are modeled by a Lorentz type operator. The main aim is to construct a discrete scheme to approximate this equation which gives for any value of the Knudsen number, and in particular at the diffusive limit, the right discrete diffusion equation with the same value of the diffusion coefficient as in the continuous case. We are also naturally interested with a discretization which can be used with few velocity discretization points, in order to reduce the cost of computation.
LA - eng
KW - Hilbert expansion; diffusion limit.; diffusion limit
UR - http://eudml.org/doc/194119
ER -

References

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