2019/07/22 by Samuele Rubino, Rubino, Samuele · 1 citation
Engineering · Mathematics · Physics and Astronomy · #65M12 #65M15 #65M60 #76D03 #76D05 #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1907.09213
openalex publication_date 2019/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose a new stabilized projection-based POD-ROM for the\nnumerical simulation of incompressible flows. The new method draws inspiration\nfrom successful numerical stabilization techniques used in the context of\nFinite Element (FE) methods, such as Local Projection Stabilization (LPS). In\nparticular, the new LPS-ROM is a velocity-pressure ROM that uses pressure modes\nas well to compute the reduced order pressure, needed for instance in the\ncomputation of relevant quantities, such as drag and lift forces on bodies in\nthe flow. The new LPS-ROM circumvents the standard discrete inf-sup condition\nfor the POD velocity-pressure spaces, whose fulfillment can be rather expensive\nin realistic applications in Computational Fluid Dynamics (CFD). Also, the\nvelocity modes does not have to be neither strongly nor weakly divergence-free,\nwhich allows to use snapshots generated for instance with penalty or\nprojection-based stabilized methods. The numerical analysis of the fully\nNavier-Stokes discretization for the new LPS-ROM is presented, by mainly\nderiving the corresponding error estimates. Numerical studies are performed to\ndiscuss the accuracy and performance of the new LPS-ROM on a two-dimensional\nlaminar unsteady flow past a circular obstacle.\n