A nonlinear multigrid method for the three-dimensional incompressible Navier-Stokes equations (Q1275172)

We develop a nonlinear multigrid method for solving three-dimensional Navier-Stokes equations in the artificial compressibility formulation. The method is based on the full multigrid-full approximation storage algorithm and is realized via an ``unsteady-type'' procedure, according to which the equations are not solved exactly on the coarsests grid, but some pseudo-time iterations are performed on the finer grids and some on the coarsest grid. The multigrid method uses a third-order upwind characteristic-based scheme for the discretization of convection terms, and the fourth-order Runge-Kutta scheme for time integration. The performance of the method is tested on three-dimensional flows in straight and curved channels, as well as on a flow in cubic cavity.