A Robust Multigrid Method for a Discretization of the Incompressible Navier-Stokes Equations in General Coordinates

Abstract

The stationary incompressible Navier-Stokes equations are discretized with a finite volume method in curvilinear coordinates. The arbitrarily shaped domain is mapped onto a rectangular block, resulting in a boundary-fitted grid. In order to obtain accurate discretizations of the transformed equations certain requirements on geometric quantities should be met. The choice of velocity components is of importance. Contravariant flux unknowns and the pressure are used as primary unknowns on a staggered grid. The system of discretized equations is solved with a nonlinear multigrid algorithm, in which a robust line smoother, called Symmetric Coupled Alternating Lines, is implemented. All unknowns on a line of cells are updated simultaneously with alternating zebra sweeping. The solution algorithm shows satisfying average reduction factors for arbitrary domains, even when highly stretched cells are present.