title: Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution.
abstract: The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wuet al.(Wuet al. 2012Proc. R. Soc. A468, 1799-1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi-Dirac or Bose-Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas.
authors.affiliation: Institute of Applied Mechanics , National Taiwan University , Taipei 10764, Taiwan, Republic of China ; Center for Advanced Study in Theoretical Science , National Taiwan University , Taipei 10764, Taiwan, Republic of China.
authors.forename: Jaw-Yen
authors.initials: JY
authors.lastname: Yang
authors.affiliation: Institute of Applied Mechanics , National Taiwan University , Taipei 10764, Taiwan, Republic of China.
authors.forename: Chih-Yuan
authors.initials: CY
authors.lastname: Yan
authors.affiliation: Institute of Applied Mechanics , National Taiwan University , Taipei 10764, Taiwan, Republic of China.
authors.forename: Manuel
authors.initials: M
authors.lastname: Diaz
authors.affiliation: Department of Merchant Marine , National Taiwan Ocean University , Taipei 10764, Taiwan, Republic of China.
authors.forename: Juan-Chen
authors.initials: JC
authors.lastname: Huang
authors.affiliation: China Aerodynamics Research and Development Center, Mianyang 621000, People's Republic of China.
authors.forename: Zhihui
authors.initials: Z
authors.lastname: Li
authors.affiliation: China Aerodynamics Research and Development Center, Mianyang 621000, People's Republic of China.
authors.forename: Hanxin
authors.initials: H
authors.lastname: Zhang
keywords: discrete ordinate method; ellipsoidal-statistical Bhatnagar–Gross–Krook; semiclassical Boltzmann equation; total variation diminishing; two-dimensional Riemann problems