2022/05/10 by Sean Ingimarson, Monika Neda, Ingimarson, Sean +7 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2205.05160
openalex publication_date 2022/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider a pressure correction temporal discretization for the incompressible Navier-Stokes equations in EMAC form. We prove stability and error estimates for the case of mixed finite element spatial discretization, and in particular that the Gronwall constant's exponential dependence on the Reynolds number is removed (for sufficiently smooth true solutions) or at least significantly reduced compared to the commonly used skew-symmetric formulation. We also show the method preserves momentum and angular momentum, and while it does not preserve energy it does admit an energy inequality. Several numerical tests show the advantages EMAC can have over other commonly used formulations of the nonlinearity. Additionally, we discuss extensions of the results to the usual Crank-Nicolson temporal discretization.