发表机构
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对稀疏流动，提出局域高斯动力学表示方法，在激波和空腔基准测试中实现高精度，优于基线方法，为稀疏流动参数化应用提供定量准则。
AI 中文摘要
稀疏流动的紧凑表示必须保留非平衡输运信息，同时确定其有效范围。我们针对单原子正激波和顶盖驱动空腔中的离散速度法（DVM）态，研究一种常见的局域高斯策略。该策略针对可用的动力学态进行了专门适配：正相空间混合物表示激波分布并通过正交积分重构其矩层级，而共享支撑物理空间映射表示20个空腔场。局域支撑、连续评估、输运保真度及系数计数核算因此构成两个基准的共同结构。对于分别拟合的马赫3和马赫5激波，该方法在守恒量上给出亚百分比误差，在输运量和高阶矩上给出约1%至2%的误差。在相同的4608个系数预算下，所测试的多重线性网格在这些非平衡量上产生89%至98%的误差。对于两种空腔情况，高斯映射也优于匹配的双线性和奇异值分解基线，将最大误差降低约7至24倍。在马赫条件测试中，保持存储量固定时，保对应关系的局域基将未参与训练的马赫6分布误差从42.86±5.40%降至11.45±0.94%，而其输运误差仍为30%至40%；归一化坐标保护机制拒绝训练范围外的马赫12。独立网格研究证实，这些趋势并非由DVM离散化误差主导。研究结果确立局域高斯表示为存储高效的、针对拟合动力学态的输运保真度映射，并为参数化应用提供定量接受准则。
英文摘要
Compact representations of rarefied flows must retain nonequilibrium transport information while identifying their range of validity. We investigate a common localized-Gaussian strategy for discrete-velocity-method (DVM) states in monatomic normal shocks and lid-driven cavities. The strategy is specialized to the available kinetic state: a positive phase-space mixture represents shock distributions and regenerates their moment hierarchy by quadrature, whereas a shared-support physical-space map represents 20 cavity fields. Localized support, continuous evaluation, transport fidelity, and coefficient-count accounting therefore provide the common structure across the two benchmarks. For separately fitted Mach-3 and Mach-5 shocks, the method gives sub-percent errors in conserved quantities and approximately 1--2\% errors in transport and higher-order moments. At the same 4608-coefficient budget, the tested multilinear grids produce 89--98\% errors in these nonequilibrium quantities. For both cavity cases, the Gaussian map also outperforms matched bilinear and singular-value-decomposition baselines, reducing maximum errors by factors of approximately 7--24. In the Mach-conditioned tests, a correspondence-preserving local basis reduces the withheld Mach-6 distribution error from $42.86\pm5.40\%$ to $11.45\pm0.94\%$ at fixed storage, while its transport errors remain 30--40\%; a normalized-coordinate guard rejects Mach 12 outside the training range. Independent grid studies confirm that these trends are not dominated by DVM discretization error. The results establish localized Gaussian representations as storage-efficient transport-fidelity maps for fitted kinetic states and provide quantitative acceptance criteria for parametric use.
