统一气体动理学格式及其波粒方法综述

Review of unified gas-kinetic scheme and its wave-particle approach

  • 摘要: 与传统计算流体力学(CFD)受限于偏微分方程(PDE)离散化求解的固有框架不同,直接建模思想的核心是将网格尺度作为观测尺度引入数值格式的构造过程,进而在离散的时空进行多尺度建模,以实现从玻尔兹曼方程所描述的分子平均自由程尺度到纳维-斯托克斯方程所描述的宏观流体力学尺度之间任意中间尺度物理问题的准确模拟。基于该思想,徐昆及其团队先后提出了统一气体动理学格式(UGKS)及统一气体动理学波粒法(UGKWP)。其关键在于构造了依赖于时空分辨率的流体演化通量,从而突破了分子平均自由程和碰撞时间对网格尺寸和时间步长的限制。在算法实现层面,UGKS通过协同更新相空间分布函数与宏观守恒量来保证全流域的非平衡输运的准确捕捉,而UGKWP则作为其高效的波粒耦合实现方案,在保持多尺度物理特性的同时基于粒子演化实现了速度空间自适应的特征。UGKS与UGKWP最早针对高超声速和微尺度问题中的中性气体流动开展研究,鉴于不同物理系统中的非平衡输运过程存在共性的动理学特征,该方法随后被扩展应用于多组分等离子体、辐射输运、颗粒两相流及非平衡湍流建模等多个问题的研究。本文系统综述了UGKS/UGKWP方法在上述领域中的最新研究进展,以展现直接建模思想在解决跨尺度复杂物理问题时的普适性,揭示了多尺度非平衡流动研究在流体力学及相关交叉学科研究中的重要性。

     

    Abstract: Unlike traditional computational fluid dynamics (CFD), which is constrained by the conventional framework of discretizing partial differential equations (PDEs), the core idea of direct modeling approach is the integration of the cell-grid size as the observational scale into the construction of discrete numerical schemes, allowing for accurate simulation of physical problems at any intermediate scale between the molecular mean-free-path scale described by the Boltzmann equation and the macroscopic fluid mechanics scale described by the Navier-Stokes equations. Based on this idea, Xu and his team have proposed the Unified Gas-Kinetic Scheme (UGKS) and the Unified Gas-Kinetic Wave-Particle method (UGKWP). The key lies in constructing the time-dependent evolution fluxes, thereby overcoming the constraints imposed by molecular mean free path and collision time on grid size and time step. UGKS ensures accurate capture of non-equilibrium transport across all flow regimes by co-updating the distribution function and macroscopic conserved quantities; in contrast, UGKWP, the efficient wave-particle implementation of UGKS, preserves multiscale physical features while achieving velocity-space adaptive features through particle evolution. Initially developed for hypersonic and microscale gas flows, UGKS and UGKWP have subsequently been extended to other problems with non-equilibrium transport feature, including multi-component plasma, radiation transport, particle-laden two-phase flows, and non-equilibrium turbulence modeling, etc. This paper systematically reviews the latest progress of UGKS/UGKWP methods in the aforementioned fields, aiming to demonstrate the generalizability of the direct modeling approach in addressing multiscale problems and highlights the importance of multiscale non-equilibrium flow in fluid mechanics and related interdisciplinary fields.

     

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