2020/05/06 by Denis Sipp, Sipp, Denis, Miguel Fosas de Pando +3
Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Vibration Analysis #Hydraulic and Pneumatic Systems #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2005.03173
openalex publication_date 2020/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Several nonlinear model reduction techniques are compared for the three cases\nof the non-parallel version of the Kuramoto-Sivashinsky equation, the transient\nregime of flow past a cylinder at Re=100 and fully developed flow past a\ncylinder at the same Reynolds number. The linear terms of the governing\nequations are reduced by Galerkin projection onto a POD basis of the flow\nstate, while the reduced nonlinear convection terms are obtained either by a\nGalerkin projection onto the same state basis, by a Galerkin projection onto a\nPOD basis representing the nonlinearities or by applying the Discrete Empirical\nInterpolation Method (DEIM) to a POD basis of the nonlinearities. The quality\nof the reduced order models is assessed as to their stability, accuracy and\nrobustness, and appropriate quantitative measures are introduced and compared.\nIn particular, the properties of the reduced linear terms are compared to those\nof the full-scale terms, and the structure of the nonlinear quadratic terms is\nanalyzed as to the conservation of kinetic energy. It is shown that all three\nreduction techniques provide excellent and similar results for the cases of the\nKuramoto-Sivashinsky equation and the limit-cycle cylinder flow. For the case\nof the transient regime of flow past a cylinder, only the pure Galerkin\ntechniques are successful, while the DEIM technique produces reduced-order\nmodels that diverge in finite time.\n