Commun. Comput. Phys., 10 (2011), pp. 405-421.

Semiclassical Lattice Boltzmann Simulations of Rarefied Circular Pipe Flows

Jaw-Yen Yang 1*, Li-Hsin Hung 2, Yao-Tien Kuo 2

1 Center for Quantum Science and Engineering and Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan.
2 Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan.

Received 6 February 2010; Accepted (in revised version) 27 August 2010
Available online 27 April 2011


Computations of microscopic circular pipe flow in a rarefied quantum gas are presented using a semiclassical axisymmetric lattice Boltzmann method. The method is first derived by directly projecting the Uehling-Uhlenbeck Boltzmann-BGK equations in two-dimensional rectangular coordinates onto the tensor Hermite polynomials using moment expansion method and then the forcing strategy of Halliday et al. [Phys. Rev. E., 64 (2001), 011208] is adopted by adding forcing terms into the resulting microdynamic evolution equation. The determination of the forcing terms is dictated by yielding the emergent macroscopic equations toward a particular target form. The correct macroscopic equations of the incompressible axisymmetric viscous flows are recovered through the Chapman-Enskog expansion. The velocity profiles and the mass flow rates of pipe flows with several Knudsen numbers covering different flow regimes are presented. It is found the Knudsen minimum can be captured in all three statistics studied. The results also indicate distinct characteristics of the effects of quantum statistics.

AMS subject classifications: 76P05, 82B40, 82D05, 82C40
PACS: 47.11.-j, 51.10.+y, 47.45.Ab, 67.10.Jn
Key words: Semiclassical lattice Boltzmann method, axisymmetric flows, rarefied pipe flow, Knudsen minimum.

*Corresponding author.
Email: (J.-Y. Yang), (L.-H. Hung), (Y.-T. Kuo)

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