A POD-Galerkin reduced order model for the Navier–Stokes equations in stream function-vorticity formulation

• Published in: Computers & Fluids
• Main Authors: Girfoglio M., Quaini A., Rozza G.
• Other Authors: Girfoglio, M., Quaini, A., Rozza, G.
• Format: Article in Journal/Newspaper
• Language: English
• Published: 2022
• Subjects: Galerkin projection; Navier–stokes equation; Proper orthogonal decomposition; Reduced order model; Stream function-vorticity formulation; Settore MAT/08 - Analisi Numerica; North Atlantic
• Online Access: https://hdl.handle.net/20.500.11767/129110; https://doi.org/10.1016/j.compfluid.2022.105536; https://arxiv.org/abs/2201.00756

We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier–Stokes equations in the stream function-vorticity formulation. Unlike previous works, we choose different reduced coefficients for the vorticity and stream function fields. In addition, for parametric studies we use a global POD basis space obtained from a database of time dependent full order snapshots related to sample points in the parameter space. We test the performance of our ROM strategy with the well-known vortex merger benchmark and a more complex case study featuring the geometry of the North Atlantic Ocean. Accuracy and efficiency are assessed for both time reconstruction and physical parameterization.