Simulation of Microchannel Flows Using a Semiclassical Lattice Boltzmann Method

The 2-D microchannel flow of gas of arbitrary statistics is simulated using a newly developed semiclassical lattice Boltzmann method based on quantum kinetic theory. The method is directly derived by projecting the Uehling-Uhlenbeck Boltzmann-BGK equations onto the tensor Hermite polynomials using moment expansion method. The intrinsic discrete nodes of the Gauss-Hermite quadrature provide the natural lattice velocities for the semiclassical lattice Boltzmann method. The mass flow rates and the velocity profiles are calculated for the three particle statistics over wide range of Knudsen numbers. In particular, the Knudsen minimum can be captured in a rarefied quantum gas microchannel flow. The results indicate distinct characteristics of the effects of quantum statistics.