Diffusion limit of the Lorentz model : asymptotic preserving schemes
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 4, p. 631-655

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.

DOI : https://doi.org/10.1051/m2an:2002028
Classification:  82C70,  35B40,  65N06
Keywords: Hilbert expansion, diffusion limit
@article{M2AN_2002__36_4_631_0,
     author = {Buet, Christophe and Cordier, St\'ephane and Lucquin-Desreux, Brigitte and Mancini, Simona},
     title = {Diffusion limit of the Lorentz model : asymptotic preserving schemes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {4},
     year = {2002},
     pages = {631-655},
     doi = {10.1051/m2an:2002028},
     zbl = {1062.82050},
     mrnumber = {1932307},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2002__36_4_631_0}
}
Buet, Christophe; Cordier, Stéphane; Lucquin-Desreux, Brigitte; Mancini, Simona. Diffusion limit of the Lorentz model : asymptotic preserving schemes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 4, pp. 631-655. doi : 10.1051/m2an:2002028. http://www.numdam.org/item/M2AN_2002__36_4_631_0/

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