title: Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation.
abstract: Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied.
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: Chin-Yuan
authors.initials: CY
authors.lastname: Yan
authors.affiliation: Department of Merchant Marine , National Taiwan Ocean University , Keelung 20224, 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
keywords: discrete-ordinate method; ellipsoidal-statistical Bhatnagar–Gross–Krook; rarefied quantum gas flows; semiclassical Boltzmann equation
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