Large Eddy Simulation: Mathematical theory and Numerical Analysis

大涡模拟被广泛认为是模拟湍流最有前途的方法，其数学验证和发展对其进一步发展具有重要意义。目前的涡流黏度模型在长时间模拟中用处有限，因为它们会使大型结构过度扩散。它们的准确性有限，因为它们与湍流涨落物理学的联系很微弱。Layton将首先测试一种改进的涡流粘度模型，该模型来自于对所涉及的物理过程的更仔细的数学描述，并且比Smagorinsky模型的弥漫性更小。涡流粘度只作用于最细的已分解尺度的第二个概念将被研究。大多数现有的反卷积模型受到高频不正确的欠衰减和不正确的全局动能平衡的限制。提出的反卷积模型研究将寻求纠正这两个困难。目前使用的粗糙的近壁模型严重限制了LES在工业应用中的实用性。Layton开发了改进的通道流动的近壁模型，具有正确的双渐近性（Re -∞和delta - 0）。这些将被扩展到产生适合再循环流动的非线性近壁模型。Layton还将研究一种新的变分多尺度方法，该方法基于流体应力的多尺度分解，而不是流体速度。莱顿建议继续大涡模拟的数学发展。大涡流模拟解决了预测问题，利用数学分析，物理建模和高性能计算，在高雷诺数的流体流动中，大的，高能的涡流（或漩涡）。这个问题是全球变化研究、地球物理和环境、航空航天应用甚至人工心脏设计等许多重要应用中的核心难题。大涡模拟被广泛认为是模拟湍流最有前途的方法，其数学验证和发展对其进一步发展具有重要意义。本文旨在通过深入的数学分析，改进涡流黏度模型、反卷积模型和近壁模型。

Large eddy simulation is widely considered to be the most promising approach to simulating turbulence and its mathematical validation and development are important to its further evolution. Current eddy-viscosity models are of limited usefulness in long time simulations because they can overly diffuse the large structures. They are of limited accuracy because their connection to the physics of turbulent fluctuations is tenuous. Layton will first test an improved eddy viscosity model which arises from a more careful mathematical description of the involved physical processes and which is less diffusive than the Smagorinsky model. A second idea of eddy viscosity acting only on the finest resolved scales will be investigated. Most present de-convolution models are limited by an incorrect under-attenuation of high frequencies and an incorrect global kinetic energy balance. The proposed research on de-convolution models will seek to correct both difficulties. The usefulness of LES in industrial applications is severely limited by the crude near wall models currently used. Layton has developed improved near wall models for channel flow with the correct double-asymptotics (Re - infinity and delta - 0). These will be extended to produce nonlinear near wall models suitable for recirculating flows. Layton will also investigate a new variational multiscale method based on a multiscale decomposition of the fluid stresses rather than fluid velocities.Layton proposes to continue the mathematical development of large eddy simulation. Large eddy simulation addresses the problem of predicting, using mathematical analysis, physical modeling and high performance computing, the large, energetic eddies (or swirls) in the flow of fluids at high Reynolds numbers. This problem is a core difficulty in many important applications such as global change studies, geophysics and the environment, aeronautics and aerospace applications and even in the design of artificial hearts. Large eddy simulation is widely considered to be the most promising approach to simulating turbulence and its mathematical validation and development is important to its further evolution. This proposal aims to improve eddy-viscosity models, de-convolution models, and near-wall models by a thorough mathematical analysis.