Year: 2012
Communications in Computational Physics, Vol. 12 (2012), Iss. 5 : pp. 1541–1561
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.220411.090112a
Communications in Computational Physics, Vol. 12 (2012), Iss. 5 : pp. 1541–1561
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
-
A BGK‐penalization‐based asymptotic‐preserving scheme for the multispecies Boltzmann equation
Jin, Shi | Li, QinNumerical Methods for Partial Differential Equations, Vol. 29 (2013), Iss. 3 P.1056
https://doi.org/10.1002/num.21746 [Citations: 16] -
Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues
Asymptotic-Preserving Schemes for Multiscale Hyperbolic and Kinetic Equations
Hu, J. | Jin, S. | Li, Q.2017
https://doi.org/10.1016/bs.hna.2016.09.001 [Citations: 19] -
Asymptotic-Preserving Numerical Schemes for the Semiconductor Boltzmann Equation Efficient in the High Field Regime
Jin, Shi | Wang, LiSIAM Journal on Scientific Computing, Vol. 35 (2013), Iss. 3 P.B799
https://doi.org/10.1137/120886534 [Citations: 12] -
Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma
Scullard, Christian R. | Belt, Andrew P. | Fennell, Susan C. | Janković, Marija R. | Ng, Nathan | Serna, Susana | Graziani, Frank R.Physics of Plasmas, Vol. 23 (2016), Iss. 9
https://doi.org/10.1063/1.4963254 [Citations: 7] -
Asymptotic-Preserving Exponential Methods for the Quantum Boltzmann Equation with High-Order Accuracy
Hu, Jingwei | Li, Qin | Pareschi, LorenzoJournal of Scientific Computing, Vol. 62 (2015), Iss. 2 P.555
https://doi.org/10.1007/s10915-014-9869-2 [Citations: 6] -
A Successive Penalty-Based Asymptotic-Preserving Scheme for Kinetic Equations
Yan, Bokai | Jin, ShiSIAM Journal on Scientific Computing, Vol. 35 (2013), Iss. 1 P.A150
https://doi.org/10.1137/110857982 [Citations: 18] -
On stochastic Galerkin approximation of the nonlinear Boltzmann equation with uncertainty in the fluid regime
Hu, Jingwei | Jin, Shi | Shu, RuiwenJournal of Computational Physics, Vol. 397 (2019), Iss. P.108838
https://doi.org/10.1016/j.jcp.2019.07.037 [Citations: 8] -
On the quantum Landau collision operator and electron collisions in dense plasmas
Daligault, Jérôme
Physics of Plasmas, Vol. 23 (2016), Iss. 3
https://doi.org/10.1063/1.4944392 [Citations: 18] -
A Vlasov-Fokker-Planck-Landau code for the simulation of colliding supersonic dense plasma flows
Zhao, Hanzhi | Weng, Suming | Sheng, Zhengming | Jin, Shi | Zhang, JieJournal of Computational Physics, Vol. 503 (2024), Iss. P.112843
https://doi.org/10.1016/j.jcp.2024.112843 [Citations: 0] -
Asymptotic-preserving schemes for multiscale physical problems
Jin, Shi
Acta Numerica, Vol. 31 (2022), Iss. P.415
https://doi.org/10.1017/S0962492922000010 [Citations: 30] -
Quantum Fokker-Planck modeling of degenerate electrons
Le, Hai P.
Journal of Computational Physics, Vol. 434 (2021), Iss. P.110230
https://doi.org/10.1016/j.jcp.2021.110230 [Citations: 1] -
Integral propagator method as a kinetic operator to describe discontinuous plasmas
Donoso, J. M. | Jimenez, A. | Gonzalez, J. | Conde, L.Journal of Physics: Conference Series, Vol. 768 (2016), Iss. P.012004
https://doi.org/10.1088/1742-6596/768/1/012004 [Citations: 0] -
Solving Vlasov-Poisson-Fokker-Planck Equations using NRxx method
Wang, Yanli | Zhang, ShudaoCommunications in Computational Physics, Vol. 21 (2017), Iss. 3 P.782
https://doi.org/10.4208/cicp.220415.080816a [Citations: 4]