(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
A semiclassical lattice Boltzmann method is presented for axisymmetric flows of gas of particles of arbitrary statistics. 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 and forcing term is added 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. Computations of uniform flow over a sphere to verify the method are included. The results also indicate distinct characteristics of the effects of quantum statistics.