Asymptotic Preserving Schemes for Semiconductor Boltzmann Equation in the Diffusive Regime

Asymptotic Preserving Schemes for Semiconductor Boltzmann Equation in the Diffusive Regime

Year:    2012

Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 2 : pp. 278–296

Abstract

As is known, the numerical stiffness arising from the small mean free path is one of the main difficulties in the kinetic equations. In this paper, we derive both the split and the unsplit schemes for the linear semiconductor Boltzmann equation with a diffusive scaling. In the two schemes, the anisotropic collision operator is realized by the "BGK"-penalty method, which is proposed by Filbet and Jin [F. Filbet and S. Jin, J. Comp. Phys. 229(20), 7625-7648, 2010] for the kinetic equations and the related problems having stiff sources. According to the numerical results, both of the schemes are shown to be uniformly convergent and asymptotic-preserving. Besides, numerical evidences suggest that the unsplit scheme has a better numerical stability than the split scheme.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2012.m1045

Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 2 : pp. 278–296

Published online:    2012-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    linear semiconductor Boltzmann equation drift-diffusion limit diffusive relaxation system "BGK"-penalty method.