发表机构
School of Mathematics and Statistics, Huazhong University of Science and Technology; State Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology; Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology（华中科技大学数学与统计学院; 华中科技大学能源与动力工程学院煤炭燃烧国家重点实验室; 华中科技大学数学与应用科学交叉研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出矢量离散统一气体动理学格式（V-DUGKS），通过耦合分布函数与独立松弛实现可调普朗特数，采用二阶厄米特截断和紧凑速度集，在保证精度的同时提升效率，数值测试显示三维涡流加速2.2-2.9倍。
AI 中文摘要
针对连续可压缩流，提出了一种矢量离散统一气体动理学格式（V-DUGKS）。在矢量动理学框架中，质量、动量和总能量由耦合的分布函数表示，动量和能量输运分别采用独立的松弛过程，从而能够调节普朗特数。所有平衡分布均截断至二阶厄米特（Hermite）阶。由于仅需二阶速度矩即可恢复可压缩纳维-斯托克斯方程，四阶高斯-厄米特求积足以实现精确的矩评估。消除三阶厄米特项后，所有分布函数可统一使用紧凑的离散速度集合，降低了对数值参考温度的敏感性，并在稳定性和效率上优于标量DUGKS。该格式采用有限体积公式，基于特征的通量评估和梯形碰撞积分。数值测试包括激波管、Shu-Osher、二维黎曼和三维泰勒-格林涡问题，验证了其准确性和鲁棒性。对于三维泰勒-格林涡，在相同CFL约束下，V-DUGKS由于允许更大的时间步长和简化的平衡公式，实现了约2.2-2.9倍的加速。这些结果表明，V-DUGKS为连续可压缩流模拟提供了一个鲁棒且高效的动理学框架。
英文摘要
A vectorial discrete unified gas kinetic scheme (V-DUGKS) is proposed for continuum compressible flows. In the vectorial kinetic framework, mass, momentum, and total energy are represented by coupled distribution functions with separate relaxation processes for momentum and energy transport, enabling an adjustable Prandtl number. All equilibrium distributions are truncated at the second-order Hermite level. Since only second-order velocity moments are required to recover the compressible Navier-Stokes equations, fourth-order Gauss-Hermite quadrature is sufficient for exact moment evaluation. Eliminating third-order Hermite terms allows compact discrete velocity sets to be used uniformly for all distribution functions, reducing sensitivity to the numerical reference temperature and improving stability and efficiency over the scalar DUGKS. The scheme employs a finite-volume formulation with characteristic-based flux evaluation and trapezoidal collision integration. Numerical tests, including shock-tube, Shu-Osher, two-dimensional Riemann, and three-dimensional Taylor-Green vortex problems, demonstrate its accuracy and robustness. For the three-dimensional Taylor-Green vortex, V-DUGKS achieves a speed-up of about 2.2-2.9 under the same CFL constraint due to a larger allowable time step and simplified equilibrium formulation. These results show that V-DUGKS provides a robust and efficient kinetic framework for continuum compressible flow simulations.
