Mathematical Development of Large Eddy Simulation of Turbulence

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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.