基于气体动理论的湍流多尺度模拟方法研究

It is important for either theoretic studies or engineering applications to develop a multiscale method which can achieve smooth transition between physical models according to computational cell size. It is capable of effective balancing the limited computational resource and the requirement of fine simulation in the investigation of multiscale flow such as turbulence. The objective of present proposal is to develop a new multiscale method for compressible turbulence simulation, based on the mesoscopic gas-kinetic theory. The research includes three parts. The first is the improvement of existing high-order accurate gas-kinetic scheme to further increase the accuracy and resolution. The second part is to construct a new framework for multiscale simulation of turbulence with the help of cross-scale evolution solution of the expanded BGK equation, and then combine it with traditional RANS and LES models for validation and application in typical high-Reynolds-number flow. The last part of the present study is the development of turbulence model based on gas-kinetic theory and flow field data from direct numerical simulation.

发展能自动随网格尺度变化而光滑切换物理模型的多尺度方法具有非常重要的理论研究和工程应用价值。对湍流这种典型多尺度流动问题它能有效兼顾有限计算资源和流动精细模拟需求。本项目基于介观气体动理论，发展一种可压缩湍流新型多尺度模拟方法。研究内容包括：发展和改进已有高精度气体动理学格式，提高格式的精度和分辨率；利用拓展BGK方程的跨尺度演化解，构造多尺度湍流模拟新框架，结合已有RANS和LES模型加以验证，并应用到典型高雷诺数工程湍流精细模拟；从气体动理论出发，结合典型流场数据，改进和发展湍流模型。

对湍流这种典型多尺度流动问题，多尺度方法能自动随网格尺度变化而光滑切换物理模型，从而有效兼顾有限计算资源和精细模拟需求，对其开展研究具有重要的理论意义和工程应用价值。本项目基于介观气体动理学发展了高效的湍流模拟方法。首先将色散最小/耗散可控重构技术（MDCD）拓展到了非均匀网格，进而将其应用到气体动理学格式（GKS），提高了对湍流多尺度结构的分辨能力。在此基础上，结合已有DES和IDDES模型建立了传统多尺度模拟动理学方法。进而利用拓展BGK方程的跨尺度演化解，提出了一种新型的湍流多尺度模拟框架，并结合已有RANS和LES模型建立了多尺度模拟方法MS-GKS。在多种典型流动模拟中，MS-GKS显示了对湍流场的高效模拟能力。此外，还进一步结合高效紧致重构方法和GKS通量求解器，发展了非结构网格上的多种高阶精度格式，为后续发展非结构网格上的MS-GKS奠定基础。