Approximate inner solvers for block preconditioning of the incompressible Navier–Stokes problems discretized by isogeometric analysis

We deal with efficient numerical solution of the steady incompressible Navier–Stokes equations (NSE) using our in-house solver based on the isogeometric analysis (IgA) approach. We are interested in the solution of the arising saddle-point linear systems using preconditioned Krylov subspace methods. Based on our comparison of ideal versions of several state-of-the-art block preconditioners for linear systems arising from the IgA discretization of the incompressible NSE, suitable candidates have been selected. In the present paper, we focus on selecting efficient approximate solvers for solving subsystems within these preconditioning methods. We investigate the impact on the convergence of the outer solver and aim to identify an effective combination. For this purpose, we compare convergence properties of the selected solution approaches for problems with different viscosity values, mesh refinement levels and discretization bases.