Multigrid methods with PSTS- and HSS-smoothers for solving the unsteady Navier-Stokes equations

Multigrid methods are considered for staggered grid discretizations of the incompressible unsteady Navier-Stokes equations. After discretization and linearization of the problem, systems of linear algebraic equations with a strongly nonsymmetric matrix appear. Product-type skew-Hermitian triangular splitting and Hermitian/skew-Hermitian splitting methods are used as smoothers in the multigrid methods for solving the linear equation systems. Numerical experiments on a 2-D model problem were carried out using algebraic multigrid methods and indicated that these smoothers are robust with respect to the different Reynolds numbers.