大涡模拟方法是湍流数值模拟方法之一，它被认为是非常具有发展前景的数值模拟方法，未来非常有希望通过大涡模拟来实现对高雷诺数的复杂边界湍流问题的高精度模拟。目前大涡模拟方法已经被广泛应用于科学研究以及工程模拟的复杂湍流问题中，比如大气湍流、航空航天发动机、超新星爆发及高超声速飞行器等。而目前的大涡模拟的亚格子模型存在一定的缺陷，经典的涡粘模型计算稳定但与真实的亚格子项如亚格子应力的相关性较差；而计算精度较高的尺度相似模型与梯度模型的计算过程不稳定，鲁棒性较差；可以在一定程度弥补亚格子模型缺陷的传统动态方法，在复杂边界流动中的使用存在着挑战。对于可压缩问题，可压缩形式的亚格子模型多数是直接将不可压缩形式的模型推广到可压缩流动中得到的，在遇到强激波时，往往得不到很好的预测结果。比如在激波/湍流边界层干扰问题中，往往出现高阻力及高热流等问题，对飞行器的设计带来了很多挑战，目前大涡模拟的亚格子模型对这类问题的预测，往往达不到预期的效果。

本文主要开展对亚格子模型的建模与应用研究，使用理论推导及先验分析等多种方式，从物理结构和物理约束两个角度出发，提出了四种亚格子模型，对模型进行了测试并在复杂湍流的算例中进行了应用：

1. 第一类模型是从物理结构出发，在模型中考虑了螺旋度的效应。螺旋度是三维湍流中的二次无粘不变量之一，在三维湍流中同时存在着能量级串和螺旋度级串，而相对于动能来说，螺旋度可以反映流场的物理结构，比如涡盘绕、涡打结等。物理结构在湍流问题中非常关键。基于螺旋度效应构造的亚格子模型，在一定程度上可以反映物理结构，对大涡模拟在复杂流动中的应用具有积极意义。这类模型之一是针对旋转湍流，基于涡量梯度张量提出了一种新型的亚格子涡粘模型，新模型在近壁处具有正确的行为，模型中显含旋转张量且模型可以反映螺旋度耗散，可以考虑旋转中螺旋度的影响；新模型被应用在了展向旋转槽道中，可以准确预测平均速度剖面、湍流强度等关键量，并很好地预测得到展向旋转槽道中 Taylor-Görtler 涡。基于物理结构构造的第二个模型是直接对螺旋度的建模，提出了亚格子螺旋度一方程模型，推导了亚格子螺旋度的输运方程，并且对方程右端的未封闭项分别建模。该模型被应用于均匀各向同性湍流及不同雷诺数的槽道流动中，取得了很好的预测效果，相对于传统模型，新模型可以得到更丰富的流场结构。

2. 第二类模型从物理约束的角度出发，采用关键物理量来约束亚格子涡粘模型的系数。这类模型之一是改进的壁面自适应的亚格子模型。壁面自适应的当地亚格子涡粘模型被认为具有正确的壁面行为且计算非常稳定，可以预测转捩流动，但其耗散过大。针对这一问题，使用最小耗散模型来约束壁面自适应的当地亚格子模型，并且对其各向同性部分进行建模，使其更适应可压缩流动。改进的模型被应用在了可压缩槽道及激波/湍流边界层干扰流动中，新模型可以准确预测平均速度剖面等平均量，而且可以得到准确的分离泡。另一个基于物理约束的模型是准动态的亚格子动能一方程模型。该模型使用亚格子动能及亚格子能流来约束亚格子应力模型来得到其系数，并将该过程推广到了不同的亚格子通量项如亚格子热流等，形成了一套可以动态求解模型系数的方法，该方法得到的亚格子通量项与真实亚格子通量项相关性高且计算稳定，更方便在复杂边界流动中使用，可以为大涡模拟在复杂边界湍流的应用奠定基础。该方法被应用于可压缩槽道、平板边界层转捩流动、界面不稳定性等多种不同算例中，取得了相对于传统动态方法精度更高的结果。

3. 大涡模拟在高超声速流动问题的预测中扮演着十分重要的角色，本文使用准动态的亚格子动能一方程模型对高超声速激波/湍流边界层干扰、升力体标模进行了大涡模拟的计算，给出关键的摩擦阻力系数、热流系数等一系列结果，并分析得到升力体转捩的影响因素。

Large-eddy simulation (LES) is one of numerical simulation methods and is considered to accomplish high precision simulations for high Reynolds number complex turbulent flows in future. LES has been more and more applied to science researches and engineering simulations, especially in complex turbulent flows, such as atmospheric flow, aerospace engines, supernovae explosion, hypersonic vehicles. The current subgrid-scale (SGS) models have some defects for some specific problems. The classical eddyviscosity models are stable when they are applied to simulation, but the SGS stress obtained from eddy-viscosity models has low correlation with the real SGS stress. The structural models such as scale-similarity model and tensor diffusivity model can obtain the value of SGS stress which is highly correlated with the real SGS stress, but they are  unstable and have poor robustness. The dynamic procedure, which can obtain the coefficients of models through the Germano identity, can make up for the defects of SGS models. But the dynamic procedure poses challenges for the applications in complex boundary flows. For the compressible flows, the SGS models applied in compressible flows are extended from the forms in incompressible flows. When the SGS models are applied in problems such as strong shock waves, they are often not well predicted. For example, in the shock wave/turbulent boundary layer interaction problems, high Friction force and heat flux often appear, which brings many challenges to the design of aircraft. The expected predictions of the current SGS models for such problems cannot be obtained.

This paper mainly carries out modeling and application research on SGS model. Using theoretical derivation and analysis, four SGS models are proposed based on physical structures and physical constraint. These SGS models are tested in different cases and the LES in complex turbulent flows cases is supplied:

1. The first type of model is based on the physical structure and takes into account the effect of helicity in the model. Helicity is one of the secondary quadratic inviscid invariants in three-dimensional turbulence. Both energy and helicity cascades exist in three-dimensional turbulence. Compared with kinetic energy, helicity can reflect the physical structure of turbulence, such as vortex winding and vortex knotting. Physical structure is critical in turbulence. The SGS model based on helicity effect can reflect the physical structure. One of this kind of models is a new SGS eddy-viscosity model based on vortex-gradient tensor for rotating turbulence. The new model has the correct behavior near the wall. The model has the rotation tensor obviously, and the model can reflect the helicity dissipation. Thus, the influence of the helicity in the rotation can be considered. The new model is applied to the spanwise rotating channel flows, which can accurately predict the key quantities such as the average velocity profile and turbulence intensity, and can well predict the Taylor-Görtler vortex in the spanwise rotating channel. Another SGS model considered the physical structures is a SGS helicity equation model based on the transfer and dissipation of the helicity. The transport equation of SGS helicity is derived, and the unclosed term on the right side of the equation is modeled respectively. The model has been applied to homogeneous turbulence and channel flows with different Reynolds numbers, and has achieved good prediction results. Compared with the traditional model, the new model can obtain more abundant flow structure.

2. The second type of SGS models uses key physical quantities to constrain SGS eddy-viscosity model to obtain coefficients of the SGS models. One of this kind of SGS models is the modified wall-adapting local eddy-viscosity model. The wall-adapting local eddy-viscosity model is considered to have correct wall behavior and good robustness, and can predict transition flow, but its dissipation is too large. To solve these problems, the minimum dissipation model is used to constrain the wall-adapting local eddy-viscosity model, and the isotropic part of the SGS stress in this model is modeled to make it more suitable for compressible flow. The modified model is applied to compressible channel and shock/turbulent boundary layer interaction flows. The new  model can accurately predict the average velocity profile and obtain the accurate separation bubble. Another model is the quasi-dynamic SGS kinetic energy equation model, which has the high correlation with the real SGS stress and good computational stability. In this model, SGS kinetic energy and SGS energy flux are used to constrain the SGS stress model to obtain its coefficients, and the process is extended to different SGS terms such as SGS heat flux. Thus, a method that can dynamically obtained the model coefficients is developed, and the quasi-dynamic process has good robustness and can obtain high correlation SGS values, which can make contributions for the application of LES in complex boundary flows. The method has been applied to compressible channel, flat-plate boundary layer flow, interface instability and so on, and the results are more accurate than the traditional dynamic method.

3. LES plays a very important role in the prediction of hypersonic flow. The quasi-dynamic subgrid-scale kinetic energy equation model is used to simulate hypersonic shock/turbulent boundary layer interaction and lifting body. A series of results, such as skin-friction coefficient, heat flux coefficient are given. And the reason of the transition for the lifting body is obtained.