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Model Order Reduction of Incompressible Turbulent Flows

Deshmukh, Rohit
http://rave.ohiolink.edu/etdc/view?acc_num=osu1471618549

Abstract Details

2016, Doctor of Philosophy, Ohio State University, Aero/Astro Engineering.
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.
Jack McNamara (Advisor)
Datta Gaitonde (Committee Member)
Ryan Gosse (Committee Member)
Joseph Hollkamp (Committee Member)
Mohammad Samimy (Committee Member)
214 p.
Aerospace Engineering
Turbulent flows; reduced order modeling; Navier-Stokes equations; nonlinear dynamics; Galerkin projection; modal decomposition; proper orthogonal decomposition; dynamic mode decomposition; sparse coding

Recommended Citations

Citations

  • Deshmukh, R. (2016). Model Order Reduction of Incompressible Turbulent Flows [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1471618549

    APA Style (7th edition)

  • Deshmukh, Rohit. Model Order Reduction of Incompressible Turbulent Flows. 2016. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1471618549.

    MLA Style (8th edition)

  • Deshmukh, Rohit. "Model Order Reduction of Incompressible Turbulent Flows." Doctoral dissertation, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1471618549

    Chicago Manual of Style (17th edition)

osu1471618549
535
© 2016, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.