An efficient solver for the incompressible Navier-Stokes equations in rotation form

We consider preconditioned iterative methods applied to discretizations of the linearized Navier-Stokes equations in two- and three-dimensional bounded domains. Both unsteady and steady flows are considered. The equations are linearized by Picard iteration. We make use of the rotation form of the momentum equations, which has several advantages from the linear algebra point of view. We focus on a preconditioning technique based on the Hermitian/skew-Hermitian splitting of the resulting nonsymmetric saddle point matrix. We show that this technique can be implemented efficiently when the rotation form is used. We study the performance of the solvers as a function of mesh size, Reynolds number, time step, and algorithm parameters. Our results indicate that fast convergence independent of problem parameters is achieved in many cases. The preconditioner appears to be especially attractive in the case of low viscosity and for unsteady problems.