An analysis of a linearly extrapolated BDF2 subgrid artificial viscosity\n method for incompressible flows

2019/10/31 by Mahir Demi̇r, Demir, Medine, Songül Kaya +1
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1910.14416

openalex publication_date 2019/10/31 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

This report extends the mathematical support of a subgrid artificial\nviscosity (SAV) method to simulate the incompressible Navier-Stokes equations\nto better performing a linearly extrapolated BDF2 (BDF2LE) time discretization.\nThe method considers the viscous term as a combination of the vorticity and the\ngrad-div stabilization term. SAV method introduces global stabilization by\nadding a term, then antidiffuses through the extra mixed variables. We present\na detailed analysis of conservation laws, including both energy and helicity\nbalance of the method. We also show that the approximate solutions of the\nmethod are unconditionally stable and optimally convergent. Several numerical\ntests are presented for validating the support of the derived theoretical\nresults.\n

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