发表机构
The Hong Kong University of Science and Technology（香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种高阶间断伽辽金离散的通用合成迭代格式（GSIS-DG），用于稀薄气体混合流动模拟，实现高阶空间精度与快速稳态收敛，并在近连续区大幅降低计算成本。
AI 中文摘要
我们针对稳态稀薄气体混合流动，开发了通用合成迭代格式（GSIS）的高阶间断伽辽金（DG）公式。由此产生的GSIS-DG方法以相同的多项式阶数对单原子气体混合物的介观动力学方程和宏观合成方程进行离散，并交替求解。动力学解为应力和热通量提供非平衡修正，而合成方程则加速向稳态的收敛。渐近分析表明，GSIS-DG无需空间网格解析分子平均自由程即可恢复连续极限。在广泛的克努森数范围内的数值结果表明，该方法具有高阶空间精度和快速的稳态收敛性，在近连续区，与传统动力学迭代相比，计算成本降低了一个数量级以上。与二阶有限体积GSIS的比较进一步表明，GSIS-DG在更粗的物理网格上以更少的总空间自由度实现了相当或更好的精度。
英文摘要
We develop a high-order discontinuous Galerkin formulation of the general synthetic iterative scheme (GSIS) for steady rarefied gas mixture flows. The resulting GSIS-DG discretizes the mesoscopic kinetic equations for monatomic gas mixtures and the macroscopic synthetic equations with the same polynomial degree and solves them alternately. The kinetic solution supplies nonequilibrium corrections to the stress and heat flux, while the synthetic equations accelerate the convergence toward the steady state. Asymptotic analysis shows that GSIS-DG recovers the continuum limit without requiring the spatial mesh to resolve the molecular mean free path. Numerical results over a wide range of Knudsen numbers demonstrate high-order spatial accuracy and rapid steady-state convergence, with more than an order-of-magnitude reduction in computational cost relative to conventional kinetic iteration in the near-continuum regime. Comparisons with second-order finite-volume GSIS further demonstrate that GSIS-DG achieves comparable or better accuracy on coarser physical meshes with fewer total spatial degrees of freedom.
