A gas-kinetic BGK scheme for semiclassical Boltzmann hydrodynamic transport

JOURNAL OF COMPUTATIONAL PHYSICS

卷:227

Article

Shi, Yu-Hsin¹  Yang, J. Y.¹ 

[1] Natl Taiwan Univ, Inst Appl Mech, Taipei 10764, Taiwan

关键词: Quantum hydrodynamics;    Gas-kinetic scheme;    Quantum gas;    Semiclassical Boltzmann equation;    Quantum Navier-Stokes solution;   

DOI  :  10.1016/j.jcp.2008.06.036

来源: Elsevier

【 摘 要 】

A class of gas-kinetic BGK schemes for solving quantum hydrodynamic transport based on the semiclassical Boltzmann equation with the relaxation time approximation is presented. The derivation is a generalization to the development of Xu [K. Xu, A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method, from gas-kinetic theory, J. Comput. Phys. 171 (2001) 289-335] for the classical gas. Both Bose-Einstein and Fermi-Dirac gases are considered. Some new features due to the quantum equilibrium distributions are delineated. The first-order Chapman-Enskog expansion of the quantum BGK-Boltzmann equation is derived. The coefficients of shear viscosity and thermal conductivity of a quantum gas are given. The van Leer's limiter is used to interpolate and construct the distribution on interface to achieve second-order accuracy. The present quantum gas-kinetic BGK scheme recovers the Xu's scheme when the classical limit is taken. Several one-dimensional quantum gas flows in a shock tube are computed to illustrate the present method. (C) 2008 Elsevier Inc. All rights reserved.

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