An asymptotic-preserving scheme for the semiconductor Boltzmann equation toward the energy-transport limit

JOURNAL OF COMPUTATIONAL PHYSICS

卷:281

Article

Hu, Jingwei¹  Wang, Li² 

[1] Univ Texas Austin, ICES, Austin, TX 78712 USA

[2] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

关键词: Semiconductor Boltzmann equation;    Energy-transport system;    Asymptotic-preserving scheme;    Fast spectral method;   

DOI  :  10.1016/j.jcp.2014.10.050

来源: Elsevier

【 摘 要 】

We design an asymptotic-preserving scheme for the semiconductor Boltzmann equation which leads to an energy-transport system for electron mass and energy as mean free path goes to zero. As opposed to the classical drift-diffusion limit where the stiff collisions are all in one scale, new difficulties arise in the two-scale stiff collision terms because the simple BGK penalization [15] fails to drive the solution to the correct limit. We propose to set up a spatially dependent threshold on the penalization of the stiffer collision operator such that the evolution of the solution resembles a Hilbert expansion at the continuous level. Formal asymptotic analysis and numerical results confirm the efficiency and accuracy of our scheme. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free