A stabilized semi-implicit Galerkin scheme for Navier–Stokes equations

By introducing a time relaxation term for the time derivative of higher frequency components, we proposed a stabilized semi-implicit Galerkin scheme for evolutionary Navier–Stokes equations in this paper. Analysis shows that such a scheme has weaker stability conditions than that of a classical semi-implicit Galerkin scheme and, when a suitable relaxation parameter σ is chosen, it generates an approximate solution with the same accuracy as the classical one. That means the proposed scheme might use a larger time step to generate a bounded approximate solution. Thus it is more suitable for long time simulations.