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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. [ABSTRACT FROM AUTHOR]

In fact, this is also true for discretizations of the NSE, which after being discretized generally loses the exact balances of most (if not all) of energy, momentum, angular momentum, helicity, and others. Keywords: Navier-Stokes equations; regularization model; conservation model; 76-10; 76D05 EN Navier-Stokes equations regularization model conservation model 76-10 76D05 1 22 22 03/11/22 20220301 NES 220301 1 Introduction The evolution of incompressible, viscous, Newtonian flow is determined by the Navier-Stokes equations (NSE), which are given by Graph HT ht (1.1) Graph HT ht (1.2) with I u i and I p i representing velocity and pressure, I f i an external force, I i the kinematic viscosity which is inversely proportional to the Reynolds number Re, and with appropriate boundary and initial conditions. [Extracted from the article]