In this work, a discrete unified gas kinetic scheme with Monte Carlo sampling applied in velocity space (DUGKS-MC) is proposed for memory reduction in rarefied flow simulations. DUGKS-MC selects discrete velocity points via Monte Carlo sampling and computes the solution via ensemble averaging of independent realizations. Unlike the original DUGKS requiring O(Nᵈ) discrete velocity points for a d-dimensional velocity space (where N represents the resolution per coordinate direction), DUGKS-MC achieves dimension-independent computational complexity while maintaining comparable accuracy. Numerical tests, including 1D shock wave structure and 2D microcavity flow, validate the method’s performance. Comparisons with the original DUGKS demonstrate that: (1) the 1D numerical tests verify the fundamental feasibility of DUGKS-MC; (2) in 2D numerical tests, DUGKS-MC maintains equivalent solution accuracy while reducing memory consumption by 70% compared to conventional DUGKS. These results demonstrate that DUGKS-MC can effectively reduce memory requirements in high-dimensional rarefied flow simulations.

Rarefied gas flow, Discrete unified gas kinetic scheme, Monte Carlo sampling, Memory reduction