The investigators study reduced-order models for distributed parameter systems with an emphasis on complex fluid flows. They seek flow-adapted reduced-order bases and methods that synthesize energy-based developments in turbulence modeling with approaches that exploit approximate inertial manifolds. Their aim is to overcome limitations of linear model reduction methods that don't accurately model the transfer of energy among time and length scales. An important part of this study is the development of efficient algorithms to compute reduced-order bases that respect the distributed data synonymous with the simulation of complex fluid flows. Many of the techniques they study can be extended to larger classes of dissipative systems.
Reduced-order modeling is required when either predictions need to be made in a timely manner, such as in weather forecasting, or when multiple high fidelity simulations are not practical, such as in product or manufacturing design. By incorporating better energy transfer among scales and utilizing the structure of the underlying mathematical model, this study aims to build better predictions and extend the range over which these reduced-order models are useful. Improved models for complex fluids would, for example, lead to better forecasting and climate predictions, better estimates of the spread of pollutants, and more integration of reduced-order modeling in the design of molds for die-casting. The investigators also have a plan for training undergraduate and graduate students in techniques of reduced-order modeling.
