@Article{CiCP-12-1541,
author = {Jingwei Hu, Shi Jin and Bokai Yan},
title = {A Numerical Scheme for the Quantum Fokker-Planck-Landau Equation Efficient in the Fluid Regime},
journal = {Communications in Computational Physics},
year = {2012},
volume = {12},
number = {5},
pages = {1541--1561},
abstract = {<p style="text-align: justify;">We construct an efficient numerical scheme for the quantum Fokker-Planck-Landau (FPL) equation that works uniformly from kinetic to fluid regimes. Such a
scheme inevitably needs an implicit discretization of the nonlinear collision operator,
which is difficult to invert. Inspired by work [9] we seek a linear operator to penalize the quantum FPL collision term Q<sub>qFPL</sub> in order to remove the stiffness induced by
the small Knudsen number. However, there is no suitable simple quantum operator
serving the purpose and for this kind of operators one has to solve the complicated
quantum Maxwellians (Bose-Einstein or Fermi-Dirac distribution). In this paper, we
propose to penalize Q<sub>qFPL</sub> by the &quot;classical&quot; linear Fokker-Planck operator. It is based
on the observation that the classical Maxwellian, with the temperature replaced by the
internal energy, has the same first five moments as the quantum Maxwellian. Numerical results for Bose and Fermi gases are presented to illustrate the efficiency of the
scheme in both fluid and kinetic regimes.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.220411.090112a},
url = {http://global-sci.org/intro/article_detail/cicp/7346.html}
}