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Analysis of three stabilized finite volume iterative methods for the steady Navier–Stokes equations

In this work, three stabilized finite volume iterative schemes for the stationary Navier–Stokes equations are considered. Under the finite volume discretization at each iterative step, the iterative scheme I consists in solving the steady Stokes problem, iterative scheme II consists in solving the stationary linearized Navier–Stokes equations and iterative scheme III consists in solving the steady Oseen equations, respectively. We discuss the stabilities and convergence of three iterative methods. The iterative schemes I and II are stable and convergent under some strong uniqueness conditions, while iterative scheme III is unconditionally stable and convergent under the uniqueness condition. Finally, some numerical results are presented to verify the performance of these iterative schemes.