离散统一气体动理学格式的一种保守多级自适应速度空间方法

中文摘要 AI 辅助

多尺度气体流动通常跨越广泛的克努森数范围，在此范围内，流动从近连续状态变化到高度稀薄且强非平衡状态。此类流动需要在整个范围内保持精确的动理学求解器。离散统一气体动理学格式（DUGKS）提供了这样一种统一描述，但其计算成本和内存消耗主要受离散速度空间大小的支配。为缓解这一瓶颈，本工作通过多级自适应速度空间离散（MLVS-DUGKS）改进了DUGKS，在保持精度和守恒性的同时减少速度空间冗余。该方法根据每个物理单元的分布函数识别其速度空间需求，然后将这些需求分组为少量具有代表性的速度空间。这种组织方式在不为每个物理单元构建独立速度空间的情况下，保持了对不同局部流动状态的敏感性。引入线性矩约束修正以维持代表性速度空间之间的离散兼容性和守恒数据传输。涵盖从近连续到高度稀薄状态的基准模拟显示，与均匀速度空间DUGKS（UVS-DUGKS）结果高度一致。对于计算要求较高的算例，平均离散速度点数减少了约一个数量级，实现了6.67至7.51倍的加速，GPU内存减少6.15至6.88倍。阈值研究进一步表明，实际计算性能由速度空间压缩与跨层耦合开销之间的平衡所决定。因此，MLVS-DUGKS为多尺度非平衡流动模拟提供了一个准确、保守且计算高效的框架。

英文摘要

Multiscale gas flows often span a wide range of Knudsen numbers, within which the flow varies from near-continuum to highly rarefied and strongly nonequilibrium states. Such flows require kinetic solvers that remain accurate across the entire range. The discrete unified gas-kinetic scheme (DUGKS) provides such a unified description, but its computational cost and memory consumption are dominated by the size of the discrete velocity space. To alleviate this bottleneck, this work improves the DUGKS with multi-level adaptive velocity-space discretization (MLVS-DUGKS), reducing velocity-space redundancy while preserving accuracy and conservation. This method identify the velocity-space requirements of each physical cell from its distribution function, and then groups these requirements into a small number of representative velocity spaces. This organization retains sensitivity to different local flow states without constructing an independent velocity space for every physical cell. A linear moment-constrained correction is incorporated to maintain discrete compatibility and conservative data transfer between representative velocity spaces. Benchmark simulations spanning near-continuum to highly rarefied regimes show close agreement with the uniform-velocity-space DUGKS (UVS-DUGKS). For the computationally demanding cases, the average number of discrete velocity points is reduced by approximately one order of magnitude, yielding speedups of 6.67--7.51 and GPU-memory reductions by factors of 6.15--6.88. A threshold study further shows that the actual computational performance is governed by a balance between velocity-space compression and cross-level coupling overhead. The MLVS-DUGKS thus provides an accurate, conservative, and computationally efficient framework for multiscale nonequilibrium-flow simulations.

发表机构

• National University of Defense Technology（国防科技大学）
• National Key Laboratory of Aerospace Flow Physics（航空航天流动物理全国重点实验室）

机构由 AI 辅助整理，请以论文原文为准。

补充信息

备注

56 pages,23 figures