2020/05/30 by Julia Novo, Samuele Rubino, Novo, Julia +1 · 1 citation
Engineering · Physics and Astronomy · #35Q30 #65M12 #65M15 #65M20 #65M60 #65M70 #76B75 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2006.00211
openalex publication_date 2020/05/30 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Proper orthogonal decomposition (POD) stabilized methods for the\nNavier-Stokes equations are considered and analyzed. We consider two cases, the\ncase in which the snapshots are based on a non inf-sup stable method and the\ncase in which the snapshots are based on an inf-sup stable method. For both\ncases we construct approximations to the velocity and the pressure. For the\nfirst case, we analyze a method in which the snapshots are based on a\nstabilized scheme with equal order polynomials for the velocity and the\npressure with Local Projection Stabilization (LPS) for the gradient of the\nvelocity and the pressure. For the POD method we add the same kind of LPS\nstabilization for the gradient of the velocity and the pressure than the direct\nmethod, together with grad-div stabilization. In the second case, the snapshots\nare based on an inf-sup stable Galerkin method with grad-div stabilization and\nfor the POD model we apply also grad-div stabilization. In this case, since the\nsnapshots are discretely divergence-free, the pressure can be removed from the\nformulation of the POD approximation to the velocity. To approximate the\npressure, needed in many engineering applications, we use a supremizer pressure\nrecovery method. Error bounds with constants independent on inverse powers of\nthe viscosity parameter are proved for both methods. Numerical experiments show\nthe accuracy and performance of the schemes.\n