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Thursday, March 16 • 4:00pm - 5:30pm
Poster: Data-Driven Reduced-Order Modeling of Turbulent Flows

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Many geophysical and engineering flows are turbulent. The chaotic and inherently multi-scale nature of turbulent flows poses major theoretical and computational challenges to efforts aimed at understanding, predicting, or controlling such flows. Accurate calculations of turbulent flows require using computationally expensive Direct Numerical Simulations (DNS) or Large Eddy Simulations (LES). Finding the optimal design or devising online control strategies for turbulent systems often involve conducting numerous DNS or LES runs, which can be formidable for many problems, in spite of the ever-growing computational power.

As a result of these challenges, recent years have seen a significant interest in developing models that have lower computational complexities but retain the key dynamics and essential features of the turbulent flows. These so-called Reduced Order Models (ROMs), if accurate, can be readily used for optimal design and real-time prediction/control of turbulent flows because they are computationally tractable. Development of accurate, predictive ROMs for turbulent flows have been actively pursued in the academia and industry; however, currently no robust, effective, generally-applicable framework is available to calculate accurate ROMs for fully-turbulent systems.

Of particular interest is finding a robust and accurate data-driven framework for calculating predictive ROMs. A data-driven approach is desirable because it can be generally-applicable and cost-effective, and does not require a full understanding of the underlying physical processes, which are not well understood for turbulent flows. Statistical and stochastic modelling approaches based on Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD), Linear Inverse Modeling (LIM), and Fluctuation-Dissipation Theorem (FDT) have been extensively applied to find ROMs of turbulent flows. Ideas from big data and machine learning have also emerged in the past few years.

Currently, none of these data-driven frameworks can produce ROMs for fully-developed turbulent flows with the accuracy and robustness that is needed for real-world engineering problems. A major challenge is that the reason(s) behind these inaccuracies and failures are unknown and in general, there is a wide gap between the progress in dimension-reduction techniques for turbulent flows at the theoretical level and the applications of these techniques to fully-turbulent, complex systems. The purpose of this study is to bridge this gap.

This study consists of three steps: 1) A predictive ROM for a fully-turbulent Rayleigh-Benard convection system, which is a reasonable prototype for many geophysical and engineering flows, is calculated using a novel method that is accurate but numerically expensive and not data-driven; 2) ROMs using the data-driven methods such as DMD and FDT are calculated and then tested and compared and contrasted with the accurate ROM calculated in Step 1 to identify the sources of their (potential) shortcomings and find possible remedies; 3) The most effective data-driven method found in Step 2 is applied to data obtained from numerical simulations and/or networks of sensors to calculate predictive ROMs for turbulent flows that are of industrial interest. In this poster, we introduce the novel method that is used in Step 1 and present preliminary results from Steps 1 and 2 to show the promises of this approach.

avatar for Pedram Hassanzadeh

Pedram Hassanzadeh

Faculty, Rice University

Thursday March 16, 2017 4:00pm - 5:30pm
Exhibit Hall BRC