Stabilization of projection-based reduced order models of the Navier–Stokes
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A new method of stabilizing low-order, proper orthogonal decomposition based reduced-order models of the Navier–Stokes equations is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier–Stokes equations. It provides spatial basis functions different from the usual proper orthogonal decomposition basis function in that, in addition to optimally representing the solution, the new proposed basis functions also provide stable reduced-order models. The proposed approach is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer.
KeywordsModel order reduction Proper orthogonal decomposition Turbulence Stabilization Reduced order modeling Navier–Stokes Lid driven cavity Mixing layer Turbulence modeling
The authors would like to thank Dr. Bernd Noack at the Institute PPrime in Poitiers, France for his invaluable comments and making available to us the mixing layer data set. The first author is particularly thankful for the financial support provided by Dr. Noack during his visit to the PPrime institute.
The authors wish to acknowledge the Natural Science and Engineering Research Council of Canada (NSERC) and its associated Canada Graduate Scholarship (CGS) for their financial support.
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