Computational Algorithms for Model Reduction of Complex Flows

Virginia Polytechnic Institute And State University, Blacksburg VA

Investigators

Abstract

The investigators will study improved computational algorithms for model reduction of complex fluid flows. This research will have two main thrusts, new closure models and a parametric modeling framework. The investigators will investigate closure for models that are based on the proper orthogonal decomposition. This component of the research will leverage current developments in large eddy simulation along with two-level algorithms for efficient computational implementation. The fact that the closure models follow from both mathematical and physical arguments will allow for a methodology that generalizes to physical settings other than fluid flow. A new globalization methodology that combines more accurate local models with an interpolation framework to evaluate the models in parameter space will also be studied. The local model improvements are provided using flow sensitivity analysis and basis functions are constructed using a multidimensional Hermite interpolation method. The investigators will emphasize problems in geophysical fluid dynamics as well as flows with free convection. This research will expand the applicability of computationally efficient simulations to a wider class of fluid flows. The availability of dramatically faster simulations is important to many engineering applications including optimization and control of fluid flows, data assimilation and uncertainty quantification. Therefore, the research conducted in this project has direct application to a wide range of problems that include data assimilation in climate and weather modeling as well as simulation, optimization, and control of energy efficient buildings.