Error correction method for Navier-Stokes equations at high Reynolds numbers

In this paper, we present a new iterative method for solving the stationary Navier-Stokes equations (NSEs) at high Reynolds numbers. The method consists of first solving the NSEs by the Oseen iterative scheme and then an error correction strategy is implemented to control the error arising from the linearization of the nonlinear NSEs. The new method retains the advantage of the classical Oseen scheme, but it leads to a rapid rate of convergence and also enhances the capability for solving problems with higher Reynolds numbers. It will be shown that, under the uniqueness condition, the proposed method accelerates up to a factor of three in the convergence rate. The stability analysis and error estimate are presented. Furthermore, numerical simulations using the new method and other classical schemes are reported to verify the superior performance of the proposed method.