Semiclassical Lattice Boltzmann Simulations of Rarefied Circular Pipe Flows (Communications in Computational Physics, 2011)
Computations of microscopic circular pipe flow in a rarefied quantum gasare presented using a semiclassical axisymmetric lattice Boltzmann method. Themethod is first derived by directly projecting the Uehling-Uhlenbeck Boltzmann-BGKequations in two-dimensional rectangular coordinates onto the tensor Hermite polynomialsusing moment expansion method and then the forcing strategy of Hallidayet al. [Phys. Rev. E., 64 (2001), 011208] is adopted by adding forcing terms into theresulting microdynamic evolution equation. The determination of the forcing termsis dictated by yielding the emergent macroscopic equations toward a particular targetform. The correct macroscopic equations of the incompressible axisymmetric viscousflows are recovered through the Chapman-Enskog expansion. The velocity profilesand the mass flow rates of pipe flows with several Knudsen numbers covering differentflow regimes are presented. It is found the Knudsen minimum can be captured inall three statistics studied. The results also indicate distinct characteristics of the effectsof quantum statistics.