Kinetic flux vector splitting schemes for ideal quantum gas dynamics

Novel quantum kinetic flux vector splitting schemes are presented for the computation of ideal quantum gas dynamical flows. The quantum Boltzmann equation approach is adopted and both Bose-Einstein and Fermi-Dirac gases are considered. Formulas for one spatial dimension are first derived, and the resulting kinetic flux vector splitting scheme is tested for shock tube flows. A modified flux vector splitting based on the BGK model is also presented to reduce the numerical diffusion. Implementation of the efficient weighted essentially nonoscillatory method to yield a class of high resolution methods is also devised. Both the classical limit and the nearly degenerate limit are computed. The flow structures can all be accurately captured by the present kinetic flux vector splitting schemes. Results for one-dimensional boson gas under external potential are also included.