Mitigating ray effects in rarefied flow simulations using an ensemble-of-subproblems strategy with stochastic discrete velocities

In this work, a ensemble-of-subproblems strategy with stochastic discrete velocities is extended to deterministic methods for mitigating ray effects in rarefied flow simulations. The strategy involves performing multiple independent subproblems, each using a small set of randomly sampled velocity points, and then averaging their solutions to obtain the final result. The core idea is to ensure that the distribution function at any velocity can contribute to the final result, approximating highly refined velocity-space resolution without increasing the memory requirement in any single subproblem. We incorporate this strategy within the DUGKS framework, and the resulting method is denoted as SDV-DUGKS. To evaluate the performance of the proposed method, we compare SDV-DUGKS with the original DUGKS on several test cases: (a) the Sod shock tube problem, (b) the one-dimensional Riemann problem, (c) the two-dimensional lid-driven cavity flow, and (d) the two-dimensional Riemann problem. The results show that, in the collisionless limit $\mathrm{Kn} \to \infty$: (1) for one-dimensional compressible flows, SDV-DUGKS reduces memory usage by approximately 2/3 compared with that of the original DUGKS while achieving good agreement; (2) for two-dimensional compressible flows, SDV-DUGKS requires one to two orders of magnitude less memory than the original DUGKS while achieving good agreement. Based on these results, it can be concluded that the proposed method serves as a reliable and effective tool for mitigating ray effects in rarefied flow simulations.