In this work, in the framework of the discrete unified gas kinetic scheme, a high order off-lattice kinetic method is proposed for high speed rarefied gas flows. The velocity distribution function is expanded on the basis of the Hermite polynomial to a certain order to ensure the conservation of the corresponding moments. The sod shock tube problem and two dimensional lid-driven cavity flow in the hydrodynamic and early transition regimes are performed to assess the proposed method. In particular, the performance of third and fourth order of truncated Hermite polynomial associated with several on and off-lattice discrete velocity sets are evaluated. It is confirmed from the simulation results that, with the fourth order Hermite polynomial expansion the proposed method can accurately reproduce the thermal and fully compressible hydrodynamic flow. However, it is surprisingly found that the performance of D2Q16 is better than that of D2Q17, and is even better than those of D2Q37 and D2Q25 for flows in the early transition regime, suggesting that the even number of velocity points without the zero velocity seems to have a better capacity than the odd one in capturing rarefaction effect. This indicates that the molecular velocity space discretized without the zero velocity may be a promising way to reduce the number of velocity point.
- fluid mechanics
- discrete unified gas kinetic scheme
- compressible hydrodynamic flow