## A multigrid solver for the steady incompressible Navier-Stokes equations on curvilinear coordinate systems

A multigrid solver for the steady incompressible Navier-Stokes equations on a curvilinear grid is constructed. The Cartesian velocity components are used in the discretization of the momentum equations. A staggered, geometrically symmetric distribution of velocity components is adopted which eliminates spurious pressure oscillations and facilitates the transformation between Cartesian and co-or contra-variant velocity components. The SCGS (symmetrical collective Gauss-Seidel) relaxation scheme proposed by Vanka on a Cartesian grid is extended to this case to serve as the smoothing procedure of the multigrid solver, in both [open quotes]box[close quotes] and [open quotes]box-line[close quotes] versions. Due to the symmetric distribution of velocitymore »