Mathematical Development of Large Eddy Simulation of Turbulence

研究了紊流大涡流模拟的准确性和可靠性。对LES的研究包括建模、分析、算法开发、数值分析和计算测试。最近湍流近似卷积模型的数学发展表明，这种方法是开发精确、稳定和可预测的LES模型的绝佳途径。因此，寻找更好的LES模型的研究是基于近似卷积框架的。对模型匹配算法的研究有助于提高对模型及其数值分析的理解，从而开发出更好的算法。研究人员通过直接从Navier Stokes方程中开发模型和算法的分析基础以及模型灵敏度的计算估计来研究模拟的可靠性。培养博士生正确地为这一领域做出贡献是提议努力的很大一部分。从湍流中准确有效地模拟和提取可靠的信息是许多重要应用的核心计算挑战，包括全球变化估计，生物医学设备设计，能效改进，工业过程优化，新一代核反应堆的安全估计，污染的分散和减少以及涉及生物和化学剂分散的安全问题。上述所有应用都需要精确可靠的复杂流动数值模拟，因此在这些应用中取得进展需要高效准确的湍流模型和快速可靠的数值方法。该项目涉及湍流模型的开发和测试，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，以及对模型进行数值模拟的有效计算方法。研究的目的是提高湍流模拟的效率、可靠性和准确性，这是这些以及许多其他应用的核心难点。

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.