Commutation error in reduced order modeling of fluid flows
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Author(s)
Koc, Birgul
Mohebujjaman, Muhammad
Mou, Changhong
Iliescu, Traian
Date Issued
December 2019
Journal
Advances in Computational Mathematics
Publisher
Springer Science and Business Media LLC
Citation
Koc, Birgul et al. "Commutation error in reduced order modeling of fluid flows." Advances in Computational Mathematics 45, 5-6 (December 2019): 2587–2621 © 2019 Springer Science Business Media, LLC, part of Springer Nature
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Author's final manuscript
Abstract
For reduced order models (ROMs) of fluid flows, we investigate theoretically and computationally whether differentiation and ROM spatial filtering commute, i.e., whether the commutation error (CE) is nonzero. We study the CE for the Laplacian and two ROM filters: the ROM projection and the ROM differential filter. Furthermore, when the CE is nonzero, we investigate whether it has any significant effect on ROMs that are constructed by using spatial filtering. As numerical tests, we use the Burgers equation with viscosities ν = 10− 1 and ν = 10− 3 and a 2D flow past a circular cylinder at Reynolds numbers Re = 100 and Re = 500. Our investigation (i) measures the size of the CE in these test problems and (ii) shows that the CE has a significant effect on ROM development for high viscosities, but not so much for low viscosities.
MIT Department
Massachusetts Institute of Technology. Plasma Science and Fusion Center
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10444-019-09739-0
