Dissertation Defense: Model Order Reduction of Incompressible Unsteady Turbulent Flows

Committee Members

• Professor Jack McNamara, Chair
• Professor Datta Gaitonde
• Dr. Ryan Gosse
• Dr. Joseph Hollkamp
• Professor Mohammad Samimy

Abstract

Galerkin projection is a commonly used reduced order modeling approach; however, stability and accuracy of the resulting reduced order models are highly dependent on the modal decomposition technique used. In particular, deriving stable and accurate reduced order models from highly turbulent flow fields is challenging due to the presence of multi-scale phenomenon that cannot be ignored and are not well captured using the ubiquitous Proper Orthogonal Decomposition (POD). A truncated set of proper orthogonal modes is biased towards energy dominant, large-scale structures and results in over-prediction of kinetic energy from the corresponding reduced order model. The accumulation of energy during time-integration of a reduced order model may even cause instabilities. A modal decomposition technique that captures both the energy dominant structures and energy dissipating small scale structures is desired in order to achieve a power balance. The goal of this dissertation is to address the stability and accuracy issues by developing and examining alternative basis identification techniques. In particular, two modal decomposition methods are explored namely, sparse coding and Dynamic Mode Decomposition (DMD). Compared to Proper Orthogonal Decomposition, which seeks to truncate the basis spanning an observed data set into a small set of dominant modes, sparse coding is used to identify a compact representation that span all scales of the observed data. Dynamic mode decomposition seeks to identity bases that capture the underlying dynamics of a full order system. Each of the modal decomposition techniques (POD, Sparse, and DMD) are demonstrated for two canonical problems of an incompressible flow inside a two-dimensional lid-driven cavity and past a stationary cylinder. The constructed reduced order models are compared against the high-fidelity solutions. The sparse coding based reduced order models were found to outperform those developed using the dynamic mode and proper orthogonal decompositions. Furthermore, energy component analyses of high-fidelity and reduced order solutions indicate that the sparse models capture the rate of energy production and dissipation with greater accuracy compared to the dynamic mode and proper orthogonal decomposition based approaches. Significant computational speedups in the fluid flow predictions are obtained using the computed reduced order models as compared to the high-fidelity solvers.