Numerical Analysis of Non-Equilibrium Turbulence

这个研究项目处理许多工业和环境流动模拟中的一个核心问题。几乎所有的工程流体流动都存在着不处于统计平衡的复杂湍流。其准确的模拟对于许多关键应用至关重要，包括全球变化估计和能源效率优化。 例如，美国85%的能源是由燃烧产生的;能源效率优化需要精确模拟湍流混合。然而，有很少的数学理论，有效的模型，并没有系统的计算实践模拟湍流，不处于统计平衡。 该研究项目旨在开发数学模型和计算算法来模拟这种流动，并对新模型和算法进行严格的数值分析。 本计画将由数位研究生参与，主要研究非统计平衡状态下紊流的数值分析。 该项目的目标是将当前的模型和计算算法扩展到不处于统计平衡的湍流，允许反向散射（从波动返回到平均值的能量流）而没有负粘度，并为新模型和算法提供数学支持。 该研究将开发，分析和测试新的湍流模型适应模型在统计平衡，并将开发新的无条件非线性稳定，线性隐式数值方法，其近似。 该项目代表了一个系统的攻击建模和数值分析，广泛理解，湍流不处于统计平衡，调查基本的数学，建模和计算问题，在其预测模拟。

This research project treats a central problem in many industrial and environmental flow simulations. Complex turbulence not at statistical equilibrium occurs in almost all engineering fluid flows. Its accurate simulation is essential for many critical applications, including global change estimation and energy efficiency optimization. For example, 85% of the energy in the U.S. is generated by combustion; energy efficiency optimization requires accurate simulation of turbulent mixing. However, there is little mathematical theory, few effective models, and no systematic computational practice for simulation of turbulent flows that are not at statistical equilibrium. This research project aims to develop mathematical models and computational algorithms to simulate such flows and to conduct a rigorous numerical analysis of the new models and algorithms. Several graduate students will participate in the project.This project is to conduct research in numerical analysis on turbulence not at statistical equilibrium. The goal of the project is to extend current models and computational algorithms to turbulence not at statistical equilibrium, allowing for backscatter (energy flow from fluctuations back to means) without negative viscosities, and to develop mathematical support for the new models and algorithms. The research will develop, analyze, and test new models of turbulence adapted from models at statistical equilibrium and will develop new unconditionally nonlinearly stable, linearly implicit numerical methods for their approximation. The project represents a systematic attack on modeling and numerical analysis, broadly understood, of turbulence not at statistical equilibrium, investigating fundamental mathematical, modeling, and computational issues in its predictive simulation.