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Asymptotic Preserving Schemes for Semiconductor Boltzmann Equation in the Diffusive Regime

Published online by Cambridge University Press:  28 May 2015

Jia Deng
Jia Deng*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR. China
*
*Corresponding author.Email address:dengj04@gmail.com
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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.

Keywords

35Q2065M12linear semiconductor Boltzmann equationdrift-diffusion limitdiffusive relaxation system“BGK”-penalty method

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Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 5 , Issue 2 , May 2012, pp. 278 - 296
Copyright
Copyright © Global Science Press Limited 2012

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