Stabilized dimensional factorization preconditioner for solving incompressible Navier-Stokes equations

In this paper, we propose a stabilized dimensional factorization (SDF) preconditioner for saddle point problems arising from the discretization of Navier-Stokes equations. The idea is based on regularization, block factorization and selective approximation. The spectral properties of the preconditioned matrix are analyzed in details. Based on the analysis, we prescribe a reasonable choice of the regularization matrix W in the preconditioner. By using the connection with the RDF preconditioner, we determine the relaxation parameter α for the problems discretized by uniform grids and stretched grids, respectively. Finally, numerical experiments on the finite element discretizations of both steady and unsteady incompressible flow problems show that the SDF preconditioner is more efficient and robust than the RDF preconditioner, which has been illustrated very competitive with some existing preconditioners.