从模拟不可压缩和可压缩流动的气体动力学格式中提取的多尺度动力学无粘通量
A multi-scale kinetic inviscid flux extracted from the gas-kinetic scheme for simulating incompressible and compressible flows
摘要：
本文提出了一种动力学无粘通量（KIF）来模拟不可压缩和可压缩流动。它是在直接模拟多尺度流动行为的基础上构建的，用于气体动力学格式（GKS）、统一气体动力学格式（UGKS）、离散统一气体动力学格式（DUGKS）等。在KIF中，对于网格单元不能很好地解决的不连续性（如激波），主要采用代表自由输运机制（或微尺度机制）的动力学通量矢量分裂（KFVS）方法求解，而在其他光滑流动区域，主要采用中心格式的全热输运（TTT）方法求解。KIF中KFVS和TTT的权重由直接建模理论中的权重自动确定。提出了KIF中权值的两种选取方法，即UGKS和DUGKS中权值的选取方法。通过Sod激波管、稀疏波、平板边界层、空腔流和高超声速圆柱绕流的算例，验证了本文方法的有效性和准确性。KIF不遭受从carbuncle现象，并且不引入额外的数值粘性在光滑区域。特别是在高超声速圆柱体的情况下，它给出了一个非常尖锐和清晰的密度和温度的轮廓。KIF可以被看作是GKS的无粘-粘性分裂版本。通过这种分解，它很容易被用于传统的CFD框架。在以文献\cite{SunA}和文献\cite{ohwada2018a}为代表的基于动力学理论的数值格式中，它也可以被归为一类新的格式，只是权值由直接模拟的权值决定。
英文摘要：
A Kinetic Inviscid Flux (KIF) is proposed for simulating incompressible and compressible flows. It is constructed based on the direct modeling of multi-scale flow behaviors, which is used in the Gas-Kinetic Scheme (GKS), the Unified Gas-Kinetic Scheme (UGKS), the Discrete Unified Gas-Kinetic Scheme (DUGKS), etc.. In KIF, the discontinuities (such as the shock wave) that can not be well resolved by mesh cells are mainly solved by the Kinetic Flux Vector Splitting (KFVS) method representing the free transport mechanism (or micro-scale mechanism), while in other flow regions that are smooth, the flow behavior is solved mainly by the central-scheme-like Totally Thermalized Transport (TTT). The weights of KFVS and TTT in KIF is automatically determined by those in the theory of direct modeling. Two ways of choosing the weights in KIF are proposed, which are actually the weights adopted in the UGKS and the DUGKS, respectively. By using the test cases of Sod shock tube, rarefaction wave, the boundary layer of flat plate, the cavity flow and hypersonic flow over circular cylinder, the validity and accuracy of the present method are examined. The KIF does not suffer from the carbuncle phenomenon, and does not introduce extra numerical viscosity in smooth regions. Especially, in the case of hypersonic cylinder, it gives a quite sharp and clear density and temperature contours. The KIF can be viewed as an inviscid-viscous splitting version of the GKS. By the doing this splitting, it is easy to be used in the traditional CFD frameworks. It can also be classified as a new type in the numerical schemes based on the kinetic theory that are represented by the works in Ref. \cite{SunA} and Ref. \cite{ohwada2018a}, except the weights are determined by the weights of direct modeling.
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