Kinetic modelling of the quantum gases in the normal phase

Lei Wu, Jian-Ping Meng, Yonghao Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

Using the maximum entropy principle, a kinetic model equation is proposed to simplify the intricate collision term in the semi-classical Boltzmann equation for dilute quantum gases in the normal phase. The kinetic model equation keeps the main properties of the Boltzmann equation, including conservation of mass, momentum and energy, the entropy dissipation property, and rotational invariance. It also produces the correct Prandtl numbers for the Fermi gases. To validate the proposed model, the kinetic model equation is numerically solved in the hydrodynamic and kinetic flow regimes using the asymptotic preserving scheme. The results agree well with those of the quantum Euler and Boltzmann equations.
Original languageEnglish
Pages (from-to)1799-1823
Number of pages25
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume468
Issue number2142
Early online date7 Mar 2012
DOIs
Publication statusPublished - 8 Jun 2012

Keywords

  • semi-classical Boltzmann equation
  • Ellipsoidal statistical Bhtnagar-Gross-Krook equation
  • kinetic theory
  • quantum shock waves

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