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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 28-51, 2021/12/17
Reduced-order modeling has a long tradition in computational fluid dynamics. The ever-increasing significance of data for the synthesis of low-order models is well reflected in the recent successes of data-driven approaches such as Dynamic Mode Decomposition and Operator Inference. With this work, we discuss an approach to learning structured low-order models for incompressible flow from data that can be used for engineering studies such as control, optimization, and simulation. To that end, we utilize the intrinsic structure of the Navier-Stokes equations for incompressible flows and show that learning dynamics of the velocity and pressure can be decoupled, thus, leading to an efficient operator inference approach for learning the underlying dynamics of incompressible flows. Furthermore, we demonstrate the performance of the operator inference in learning low-order models using two benchmark problems and compare with an intrusive method, namely proper orthogonal decomposition, and other data-driven approaches.
Keywords: Computational fluid dynamics, scientific machine learning, incompressible flow, Navier-Stokes equations, operator inference