An asymptotic-preserving scheme for the semiconductor boltzmann equation with two-scale collisions: A splitting approach

Jingwei Hu, Shi Jin, Li Wang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We present a new asymptotic-preserving scheme for the semiconductor Boltzmann equation with two-scale collisions - a leading-order elastic collision together with a lower-order interparticle collision. When the mean free path is small, numerically solving this equation is prohibitively expensive due to the stiff collision terms. Furthermore, since the equilibrium solution is a (zero-momentum) Fermi-Dirac distribution resulting from joint action of both collisions, the simple BGK penalization designed for the one-scale collision [10] cannot capture the correct energy-transport limit. This problem was addressed in [13], where a thresholded BGK penalization was introduced. Here we propose an alternative based on a splitting approach. It has the advantage of treating the collisions at different scales separately, hence is free of choosing threshold and easier to implement. Formal asymptotic analysis and numerical results validate the effciency and accuracy of the proposed scheme.

Original languageEnglish (US)
Pages (from-to)707-723
Number of pages17
JournalKinetic and Related Models
Volume8
Issue number4
DOIs
StatePublished - Jan 1 2015
Externally publishedYes

Keywords

  • Asymptotic-preserving scheme
  • Energy-transport system
  • Semiconductor boltzmann equation
  • Splitting method

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