本文面向复杂湍流开展大涡模拟模型开发与应用研究，旨在提升大涡模拟 方法在多种复杂湍流场景下的模拟准确度与应用广度。具体而言，本文深入探索了转捩流动、旋转湍流、复杂构型流动及化学反应流动等关键领域，以期为大涡模拟方法的发展与应用提供更为精准和高效的解决方案，推动大涡模拟技术在复杂湍流研究中的广泛应用，为相关领域的研究和实践提供有力支持。具体研究如下：

1. 通过引入螺旋度的双通道约束，提出了一种新的面向旋转湍流的准动态一方程大涡模拟模型，该模型基于螺旋度流双通道理论，通过实施能流-螺旋度流双通道联合约束以及准动态过程求解，在获得准确的亚格子应力的情况下确保了模型系数始终处于合理范围，从而有效保证了数值稳定性。在准动态过程 中，所有被建模量的系数均通过动态求解得出，无需进行繁琐的测试滤波，这对于处理复杂几何形状及在高度扭曲的各向异性网格上的大涡模拟模拟尤为有利。 新提出的模型首先在不可压缩槽道流中进行了验证。结果表明，新提出的模型能够精准地预测包括平均速度、湍流强度、平均螺旋度及脉动螺旋度等在内的各项湍流统计量。此外，在流向旋转的可压缩环形管流中，新模型同样展现出了其出色的预测能力，相比传统大涡模拟模型，它不仅能够准确预测平均速度、温度及湍动能分布，还表现出捕捉复杂湍流结构的能力。

2. 本文还验证了所提出的新模型在高超音速旋转钝锥边界层转捩流动中的预测能力，并利用大涡模拟技术，对高超声速来流条件下旋转钝锥转捩过程进行了参数化研究，探讨了不同旋转角速度对转捩过程的影响。研究结果显示，随着旋转角速度的增加，转捩起始位置单调地向钝锥头部移动，壁面摩阻峰值单调增加。旋转工况下，Mack第二模态扰动波更难抵抗二次失稳，导致转捩提前，且旋转工况下的边界层扰动发展特征与无旋转工况存在显著差异。通过频谱分析，观察到旋转工况下第二模态向低频模态的转换及特定特征频率的存在，证实了旋转对转捩过程的影响及其机理。

3. 最后，本文详细阐述了作者开发的两套开源软件：OpenCFD-AMR 和 Flame3D，以及它们在大涡模拟复杂构型流动及化学反应流中的应用。OpenCFD-AMR借助性能可移植框架AMReX，实现了高性能异构并行，提高了软件的灵活 性和适应性，降低了用户在不同硬件平台间迁移的成本。该软件采用的块结构网格自适应加密算法通过子时间循环方法确保了时间推进的高效率和守恒性。通过双马赫反射算例，展示了自适应网格加密在捕捉激波和间断方面的强大能力， 使得能够以较小的计算代价获得感兴趣区域较高的分辨率。此外，为了处理复杂几何构型，介绍了两种浸没边界法：笛卡尔网格下的切割单元浸没边界法和一般曲线坐标系下的高阶清晰界面虚网格浸没边界法。这两种方法分别在OpenCFD-AMR以及Flame3D中实现，并通过高升力三段翼构型和X-59低音爆试验机的算例验证，展示了这两种方法在复杂几何构型大涡模拟中的准确性和处理任意复杂几何的能力。最后，本文简要介绍了化学反应流动的计算方法，并在Flame3D 中进行了验证。这展示了异构混合并行算法在处理极强刚性化学反应流方面的强大能力，为化学反应流动的高效大涡模拟提供了有力工具。

This paper focuses on the development and application of large eddy simulation (LES) models for complex turbulent flows, aiming to enhance the accuracy and versatility of LES methods in various complex turbulent flow scenarios. Specifically, we delve into key areas such as transition flow, rotating turbulence, flow over complex geometries, and chemically reacting flows, with the aim of providing more precise and efficient solutions for the development and application of LES methods. This endeavor aims to promote the widespread use of LES technology in the study of complex turbulent flows, providing robust support for research and practice in related fields. The specific research areas covered in this paper are as follows:

1. Anew quasi-dynamic one-equation LES model is introduced for rotating turbulence by incorporating a dual-channel constraint on helicity. This model, based on our recently proposed dual-channel theory of helicity, implements joint constraints on energy and helicity channels and quasi-dynamic processes for coefficient solving. By ensuring that the model coefficients remain within reasonable ranges while obtaining accurate subgrid-scale stresses, this approach effectively ensures numerical stability. In the quasi-dynamic process, coefficients for all modeled quantities are dynamically solved without the need for cumbersome filtering tests, making it particularly advantageous for LES simulations on complex geometries and highly distorted anisotropic grids. The proposed model is first validated in incompressible channel flow, demonstrating its ability to accurately predict various turbulent statistics including mean velocity, turbulence intensity, mean helicity, and fluctuating helicity. Furthermore, in compressible annular pipe flow with streamwise rotation, the new model exhibits excel lent predictive capabilities, not only accurately predicting mean velocity, temperature, and turbulent kinetic energy distributions but also demonstrating the ability to capture complex turbulent structures compared to traditional LES models.

2. The paper also validates the predictive capability of the proposed new model in the transition flow of high-speed rotating boundary layers over a blunt cone, and utilizes LES to conduct a parametric study of the transition process of rotating blunt cone boundary layers under conditions of hypersonic inflow, investigating the effects of different rotation rates on the transition process. The results show that with increasing rotation rate, the transition onset location monotonically moves towards the blunt cone head, and the peak wall shear stress monotonically increases. Under rotating conditions, the Mack second mode disturbance waves are more susceptible to secondary instability, leading to premature transition, and the development characteristics of boundary layer disturbances under rotating conditions significantly differ from those under nonrotating conditions. Through spectral analysis, the transition of the second mode to low-frequency modes and the presence of specific characteristic frequencies under rotating conditions are observed, confirming the influence of rotation on the transition process and its underlying mechanisms.

3. Finally, the paper elaborates on two open-source software packages developed by the authors: OpenCFD-AMR and Flame3D, and their applications in LES of complex geometrical flow and chemically reacting flows. OpenCFD-AMR achieves high performance heterogeneous parallelism through the AMReX framework, improving the flexibility and adaptability of the software while reducing the cost of migration between different hardware platforms for users. The software employs a block-structured grid adaptive refinement algorithm coupled with sub-time-stepping methods to ensure efficient and conservative time advancement. Through examples such as double Mach reflection, the powerful capabilities of adaptive grid refinement in capturing shocks and discontinuities are demonstrated, enabling higher resolution in regions of interest at a smaller computational cost. Additionally, two immersed boundary methods for handling complex geometries are introduced: the cut-cell immersed boundary method under Cartesian grids and the high-order sharp-interface fictitious grid immersed boundary method under general curvilinear coordinate systems. These methods are implemented in OpenCFD-AMR and Flame3D, respectively, and verified through examples such as a high-lift three-element airfoil configuration and the X-59low-boomsupersonic aircraft shape, showcasing their accuracy in simulating complex geometrical LES and their ability to handle arbitrarily complex geometries. Finally, we briefly introduce the computational methods for chemically reacting flows and validate them in Flame3D, demonstrating the powerful capabilities of heterogeneous hybrid parallel algorithms in handling highly stiff chemical reacting flows and providing a robust tool for efficient LES of chemically reacting flows.