Large Eddy Simulation: Mathematical theory and Numerical Analysis

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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.