2021/06/30 by Michele Girfoglio, Annalisa Quaini, Girfoglio, Michele +3 · 1 citation
Engineering · Physics and Astronomy · #FOS: Mathematics #Fluid Dynamics and Vibration Analysis #Hydraulic and Pneumatic Systems #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2106.15887
openalex publication_date 2021/06/30 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We present a stabilized POD-Galerkin reduced order method (ROM) for a Leray\nmodel. For the implementation of the model, we combine a two-step algorithm\ncalled Evolve-Filter (EF) with a computationally efficient finite volume\nmethod. In both steps of the EF algorithm, velocity and pressure fields are\napproximated using different POD basis and coefficients. To achieve pressure\nstabilization, we consider and compare two strategies: the pressure Poisson\nequation and the supremizer enrichment of the velocity space. We show that the\nevolve and filtered velocity spaces have to be enriched with the supremizer\nsolutions related to both evolve and filter pressure fields in order to obtain\nstable and accurate solutions with the supremizer enrichment method. We test\nour ROM approach on 2D unsteady flow past a cylinder at Reynolds number 0 <= Re\n<= 100. We find that both stabilization strategies produce comparable errors in\nthe reconstruction of the lift and drag coefficients, with the pressure Poisson\nequation method being more computationally efficient.\n