Semiclassical Lattice Boltzmann Simulations of Rarefied Circular Pipe Flows

Semiclassical Lattice Boltzmann Simulations of Rarefied Circular Pipe Flows

Year:    2011

Communications in Computational Physics, Vol. 10 (2011), Iss. 2 : pp. 405–421

Abstract

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.060210.270810a

Communications in Computational Physics, Vol. 10 (2011), Iss. 2 : pp. 405–421

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:   

  1. Kinetic numerical methods for solving the semiclassical Boltzmann-BGK equation

    Yang, Jaw-Yen

    Muljadi, Bagus Putra

    Chen, Su-Yuan

    Li, Zhi-Hui

    Computers & Fluids, Vol. 85 (2013), Iss. P.153

    https://doi.org/10.1016/j.compfluid.2012.12.013 [Citations: 3]