An iterative solver for the Oseen problem and numerical solution of incompressible Navier-Stokes equations (Q2760361)

The author considers incompressible Navier-Stokes equations. A semi-implicit discretization leads to the system of linearized Navier-Stokes equations. To construct an iterative solver, the author uses the Schur complement technique. A new non-symmetric preconditioner is developed to solve a non-symmetric problem of convection-diffusion of saddle-point type. The method has good performance for various values of viscosity. Unfortunately, the analysis of the method is not complete, and mathematically rigorous results are proved only in certain cases. With the use of a multigrid method, the author obtains a numerical solution of linearized problem.