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A Numerical Scheme for the Quantum Fokker-Planck-Landau Equation Efficient in the Fluid Regime

Published online by Cambridge University Press:  20 August 2015

Jingwei Hu ,
Shi Jin  and
Bokai Yan
Jingwei Hu*
Affiliation:
Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, 1 University Station C0200, Austin, TX 78712, USA
Shi Jin*
Affiliation:
Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI 53706, USA Department of Mathematics and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
Bokai Yan*
Affiliation:
Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI 53706, USA
*
Email address:hu@ices.utexas.edu
Corresponding author.Email address:jin@math.wisc.edu
Email address:yan@math.wisc.edu
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Abstract

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 QqFPL 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 QqFPL by the "classical" 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.

Keywords

35Q8465L0476Y05Quantum Fokker-Planck-Landau equationfluid limitasymptotic-preserving scheme
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 5 , November 2012 , pp. 1541 - 1561
Copyright
Copyright © Global Science Press Limited 2012

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