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

Jingwei  Hu; Shi Jin; Li  Wang

doi:10.3934/krm.2015.8.707

Article Contents

2015, Volume 8, Issue 4: 707-723. Doi: 10.3934/krm.2015.8.707

This issue Previous Article Energy dissipation for weak solutions of incompressible liquid crystal flows Next Article Relativistic transfer equations: Comparison principle and convergence to the non-equilibrium regime

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

1.
Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN 47907
2.
Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI 53706
3.
Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, CA 90095

Received: August 2014

Revised: April 2015

Published: December 2015

Abstract / Introduction Related Papers Cited by

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 efficiency and accuracy of the proposed scheme.

Keywords:

Mathematics Subject Classification: Primary: 65M06, 35L45, 35K15, 65Z05.

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References

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