不可压缩Kolmogorov湍流中动态亚格子模型的四维变分数据同化研究

大涡模拟(LES)是研究非定常湍流的有效工具，在涉及湍流的工程领域中发挥着重要作用。在LES中，亚格子(SGS)模型的准确性是LES成功的关键，有待进一步提高。四维变分数据同化(4D-VarDA)方法可利用条件约束将模拟流场和真实流场之间的误差最小化以获得最优模型参数，故此方法和真实湍流场相结合是SGS模型优化的一种新思路。本项目以三维不可压缩Kolmogorov湍流为研究对象，采用4D-VarDA方法并结合Germano等式对LES中的动态SGS模型(包括涡粘模型和混合模型)进行优化，以获得最优SGS模型及其对应的最优流场和统计量；揭示最优SGS模型中各物理量之间的关系；考察不同雷诺数、目标数据解析度、收敛因子和同化时间窗对优化结果的影响；比较最优SGS模型、DNS和其他常用模型的模拟结果。本项目的开展不仅可以拓展SGS模型的优化途径，还可为LES中SGS模型的改进提供实际帮助。

Large Eddy Simulation (LES) is an effective tool to investigate the unsteady turbulent flow, and plays a vital role in engineering applications. In LES, the accuracy of subgrid-scale (SGS) model is the key point to the successful implementation of LES, which needs to be furthermore improved. Four-dimensional variational data assimilation (4D-VarDA) method can minimize the discrepancy between the simulated flow fields and the real flow fields by using conditional constraints, which can obtain the optimal model parameters. The application of this method to the real turbulent flow fields is a new idea for the optimization of SGS model. In this project, the three-dimensional incompressible Kolmogorov turbulence is taken as the research object. In order to obtain the optimal SGS model and its corresponding optimal flow fields and statistics, the 4D-VarDA method and the Germano identity are adopted to optimize the dynamic SGS model (including eddy viscocity model and mixed model) in LES. The relationships between various physical quantities in the optimal SGS model are revealed; The effects of Reynolds numbers, resolutions of target data, converging factors and assimilation periods on the optimization results are investigated; The simulation results of the optimal SGS model, DNS model and other common models are compared. Eventually, the development of this project can not only develop the optimization approach of SGS model, but also provide practical help for the improvement of SGS model in LES.