  The numerical method toward the fast and accurate calculation of the dilute
quantum gas is studied by proposing the Uehing-Uhlenbeck (U-U) model equation.
In particular, the direct simulation Monte Carlo (DSMC) method is used to solve
the U-U model equation. The DSMC analysis of the U-U model equation surely
enables us to obtain the accurate thermalization using a small number of sample
particles and calculate the dilute quantum gas dynamics in practical time.
Finally, the availability of the DSMC analysis of the U-U model equation toward
the fast and accurate calculation of the dilute quantum gas is confirmed by
calculating the viscosity coefficient of the Bose gas on the basis of
Green-Kubo expression or shock layer of the dilute Bose gas around a circular
cylinder
