Mathematical Development of Large Eddy Simulation of Turbulence

研究了湍流大涡模拟（LES）的准确性和可靠性.大涡模拟的研究包括建模、分析、算法开发、数值分析和计算测试。湍流近似卷积模型的最新发展表明，这种方法是发展精确、稳定和可预测的大涡模拟模型的一条很好的途径，因此，寻找更好的大涡模拟模型的研究是建立在近似卷积框架的基础上的。模型匹配算法的研究是通过对模型的理解和数值分析来开发更好的算法。研究人员通过直接从Navier-Stokes方程和模型敏感性的计算估计开发模型和算法的分析基础来研究模拟的可靠性。培训博士在许多重要的应用中，准确有效地模拟和提取湍流的可靠信息是一个中心的计算挑战，包括全球变化估计，生物医学设备设计，能源效率的提高，工业过程的优化，新一代核反应堆的安全评估，污染扩散和减少以及涉及生物和化学剂扩散的安全问题。这些应用都要求对复杂流动进行准确可靠的数值模拟，而这些应用的进展需要高效准确的湍流模型和快速可靠的数值方法.本项目涉及湍流模型的开发和测试，该模型可以解决复杂流动建模和模拟中的基本困难，本研究研究了模型的物理和数学基础以及进行模型数值模拟的有效计算方法。 该研究的目的是提高效率，可靠性和准确性的模拟形成的核心困难，在这些和许多其他应用。

The investigator studies the accuracy and reliability of large eddysimulation (LES) of turbulent flows. The research on LES includesmodeling, analysis, algorithm development, numerical analysis, andcomputational testing. The recent mathematical development of approximatede-convolution models for turbulence shows this approach to be anexcellent path for developing accurate, stable and predictive LES models.The research on finding better LES models is thus based on the approximatede-convolution framework. The research on matching algorithms to modelsuses an improved understanding of models and their numerical analysis todevelop better algorithms. The investigators research studies reliabilityof simulations by developing analytical foundations of models andalgorithms directly from the Navier Stokes equations and by computationalestimation of model sensitivity. Training Ph.D. students properly tocontribute to this area is a large part of the proposed effort.The accurate and efficient simulation of and extraction of reliableinformation from turbulent flows is a central computational challenge inmany important applications including global change estimation, biomedicaldevice design, energy efficiency improvement, optimization of industrialprocesses, safety estimation of the new generation of nuclear reactors,pollution dispersal and abatement and security issues involving dispersalof biological and chemical agents. All the above applications requireaccurate and reliable numerical simulations of complex flows and thusprogress in these applications needs efficient and accurate models ofturbulence and fast and reliable numerical methods. This project involvesthe development and testing of models for turbulent flow which can addressessential difficulties in the modeling and simulation of complex flows.This research studies the physical and mathematical foundation of themodels as well as efficient computational methods for performing numericalsimulations of the models. The aim of the research is to advance theefficiency, reliability and accuracy of the simulations of turbulencewhich form a core difficulty in these, and many other, applications.