| 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. |
