Large Eddy Simulation in Complex Turbulent Flows with Coarse Resolution

流体流动的计算模拟对于各种技术的工程来说都是至关重要的。通常，这些模拟的实用性受到不可靠的湍流影响模型的限制。这项研究的目的是开发用于大涡模拟的模型，以便能够对复杂流动中的湍流进行实用和可靠的模拟。通过开发真正可靠和广泛适用的湍流模型，拟议的研究将在航空、推进、发电和风能等领域产生深远影响，有可能使对我们国家和社会重要的技术有很大改进。这种潜在影响的规模怎么说都不为过。此外，通过为研究生和本科生暑期实习生提供开发复杂物理系统数学模型的培训，该项目将为解决我国和世界面临的广泛复杂问题所需的高技能劳动力做出贡献。大涡模拟(LES)是可靠地预测湍流影响的最有前途的方法之一。在LES中，模拟最大尺度的湍流，同时模拟较小尺度的影响。然而，目前可用的模型对可靠的大涡模拟的分辨率要求对于技术上感兴趣的复杂湍流通常是不切实际的。本质上，对于实际应用，有必要使模拟在尽可能粗的分辨率下是可靠的，这通常违反了建立模型的假设，使得模型无效。已经开发了新的建模方法和工具，可以应对粗略解决的大涡模拟所带来的挑战。其中包括模型分裂公式，以允许子网格模型履行不同的角色，离散化感知模型公式，以解决数值离散化的影响，以及统计模型，允许预测大涡模拟的性能和优化模型。需要以多种方式对模型和工具进行推广，以便在复杂的流动应用中实现可靠的粗略解析-LES，而这种推广就是本提议的主题。通用模型将与不需要建模的直接数值模拟和实验数据进行对比测试，以评估其可靠性、局限性和分辨率要求。该项目更广泛的影响目标包括对复杂湍流可靠模型所实现的广泛技术的影响，以及在计算科学和复杂物理系统建模方面对研究生和本科生的培训。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Computational simulation of fluid flows is critical to engineering for a wide variety of technologies. Often, the utility of these simulations is limited by unreliable models for the effects of turbulence. The research proposed here is aimed at developing models for use in large eddy simulation that enable practical and reliable simulations of turbulence in complex flows. By developing truly reliable and broadly applicable turbulence models, the proposed research will have profound impacts in such fields as aeronautics, propulsion, power generation and wind energy, with the potential of enabling great improvements in technologies important to our country and society. The magnitude of this potential impact would be hard to overstate. In addition, by providing training for a graduate student and undergraduate summer interns in the development of mathematical models of complex physical systems, this project will contribute to the highly skilled workforce required to address a broad range of complex problems facing our country and the world.Large eddy simulation (LES), in which the largest scales of turbulence are simulated while the effects of smaller scales are modeled, is one of the most promising approaches to reliably predict the effects of turbulence. However, the resolution requirements for reliable LES with currently available models are generally impractical for complex turbulent flows of technological interest. In essence, for practical applications, it is necessary that the simulations be reliable for as coarse a resolution as possible, which generally violates the assumptions under which the models are formulated, rendering them invalid. New modeling approaches and tools that can address the challenges posed by coarsely resolved -LES have been developed. These include a model-splitting formulation to allow the subgrid models to fulfill different roles, discretization aware model formulations to address the effects of numerical discretization, and statistical models that allow the performance of a LES to be predicted and models to be optimized. The models and tools need to be generalized in several ways to enable reliable coarsely resolved-LES in complex flow applications, and such generalization is the subject of this proposal. Generalized models will be tested against direct numerical simulations, which require no modeling, and experimental data, to assess their reliability, limitations, and resolution requirements. The broader impact objectives of this project include the impact on a wide range of technologies enabled by reliable models for complex turbulent flows, and the training of a graduate student and undergraduate students in computational science and the modeling of complex physical systems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.