Numerical analysis of the SAV scheme for the EMAC formulation of the time-dependent Navier–Stokes equations

Abstract

In this work, motivated by the scalar auxiliary variable (SAV) method, we construct the first-order implicit–explicit type scheme for the EMAC formulation of the time-dependent Navier–Stokes equations. This scheme is linear and only requires solving a series of Stokes type equations with constant coefficients at each time step. What is more, the stability is given out without any condition on the time step, where the Gronwall’s constant does not dependent on the Reynolds number. Especially, this scheme also conserves momentum and angular momentum in the fully discrete case with only weakly enforced divergence constraint. Furthermore, we give out the priori error estimates for the velocity. Finally, we carry out several numerical tests to confirm the theoretical results and the effectiveness of the proposed scheme.