Numerical Analysis of Non-Equilibrium Turbulence

这项研究项目处理了许多工业和环境流动模拟中的一个中心问题。在几乎所有的工程流体流动中，都会出现不处于统计平衡的复杂湍流。它的准确模拟对于包括全球变化估计和能源效率优化在内的许多关键应用是必不可少的。例如，美国85%的能源是由燃烧产生的；能源效率优化需要准确的湍流混合模拟。然而，对于非统计平衡的湍流的模拟，几乎没有数学理论，有效的模型也很少，也没有系统的计算实践。这项研究项目旨在开发数学模型和计算算法来模拟这种流动，并对新的模型和算法进行严格的数值分析。将有几个研究生参加这个项目。这个项目是对非统计平衡的湍流进行数值分析的研究。该项目的目标是将当前的模型和计算算法扩展到非统计平衡的湍流，允许后向散射(从波动返回到平均值的能量流)而没有负粘度，并为新的模型和算法开发数学支持。这项研究将开发、分析和测试从统计平衡点模型改编而来的新的湍流模型，并将开发新的无条件非线性稳定的线性隐式数值方法来逼近它们。该项目代表着对不处于统计平衡状态的湍流的建模和数值分析的系统性攻击，研究其预测模拟中的基本数学、建模和计算问题。

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.