Numerical Analysis of a BDF2 finite Element Scheme for Navier-Stokes-Omega Model

In this paper, we study a second-order backward difference formula (BDF2) scheme for the Navier-Stokes-omega (NS-omega) model. By employing the stabilization scheme for space discretization and the BDF2 method for time discretization of NS-omega model, we obtain the fully discrete approximation of them. The paper provides an analysis of the unconditional stability and convergence of the approximate solutions. Furthermore, the numerical experiments are conducted to validate the theoretical findings and demonstrate the efficiency of the proposed scheme.