This paper presents an efficient multigrid solver for steady-state Navier-Stokes equations in 2D on non-staggered grids. The pressure Poisson equation formulation is used, together with a finite volume discretization. A discretization of the boundary conditions for pressure and velocities is presented. An efficient multigrid algorithm for solving the resulting discrete equations is then developed. The issue of the numerical treatment of advection is also addressed: a family of stable and accurate difference schemes for the advection-dominated flow are presented. This family includes also second order accurate schemes.
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