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.
