Abstract
The local equilibrium limit of the quantum Boltzmann equation is solved by KFVS (Kinetic Flux Vector Splitting) and kinetic beam scheme. Originally, these two schemes are applied in solving the flow of classical gas (based on Maxwell-Boltmann distribution). We extend these two methods to quantum gas (based on Bose-Einstein or Fermi-Dirac distribution). The shock tube problem is used as a numerical experiment. For two dimensional problems, the diffractions caused by shock wave passing a circular cylinder are simulated.
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