AI 中文总结
本研究将结合随机离散速度的子问题集成策略整合至DUGKS框架，提出SDV-DUGKS方法，可在不降低精度的前提下大幅减少稀薄流动模拟的内存使用，有效缓解射线效应。
AI 中文摘要
本研究将结合随机离散速度的子问题集成策略扩展至确定性方法，以缓解稀薄流动模拟中的射线效应。该策略需执行多个独立子问题，每个子问题使用一小部分随机采样的速度点，随后对其解进行平均以得到最终结果。其核心思想是确保任意速度处的分布函数都能对最终结果做出贡献，在不增加单个子问题内存需求的前提下近似实现高度精细的速度空间分辨率。我们将该策略整合至DUGKS框架中，所得方法命名为SDV-DUGKS。为评估所提方法的性能，我们在多个测试案例中将SDV-DUGKS与原始DUGKS进行对比：(a) Sod激波管问题、(b) 一维黎曼问题、(c) 二维 lid-driven cavity 流动、(d) 二维黎曼问题。结果表明，在无碰撞极限Kn→∞时：(1) 对于一维可压缩流动，SDV-DUGKS的内存使用量较原始DUGKS减少约2/3，同时能保持良好的一致性；(2) 对于二维可压缩流动，SDV-DUGKS的内存需求较原始DUGKS低1至2个数量级，同时能保持良好的一致性。基于这些结果可得出结论，所提方法是缓解稀薄流动模拟中射线效应的可靠有效工具。
英文摘要
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.
Comments21 pages, 26 figures
