Semiclassical Axisymmetric Lattice Boltzmann Method (Advances in Applied Mathematics and Mechanics, 2021)
A semiclassical lattice Boltzmann method is presented foraxisymmetric flows of gas of particles of arbitrarystatistics. The method is first derived by directly projecting theUehling-Uhlenbeck Boltzmann-BGK equations in two-dimensional rectangular coordinates onto the tensor Hermitepolynomials 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 resultingmicrodynamic evolution equation.  The determination of the forcing terms is dictated byyielding the emergent macroscopic equations toward a particular target form.The correct macroscopic equations of the incompressible axisymmetric viscousflows 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 characteristicsof the effects of quantum statistics.