A gas-kinetic BGK scheme for semiclassical Boltzmann hydrodynamic transport
- Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan (China)
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.
- OSTI ID:
- 21167735
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 22 Vol. 227; ISSN JCTPAH; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
BERNSTEIN MODE
BOLTZMANN EQUATION
GAS FLOW
HYDRODYNAMICS
MATHEMATICAL SOLUTIONS
NAVIER-STOKES EQUATIONS
ONE-DIMENSIONAL CALCULATIONS
PLASMA WAVES
QUANTUM MECHANICS
RELAXATION TIME
SEMICLASSICAL APPROXIMATION
SHOCK TUBES
THERMAL CONDUCTIVITY
TRANSPORT THEORY