Galerkin Coarse Grid Approximation for the Incompressible Navier-Stokes Equations in General Coordinates

In this paper, a part of multigrid methods, namely Galerkin coarse grid approximation, is discussed for the incompressible Navier-Stokes equations in general coordinates, for twodimensional problems. Some possible prolongations and restrictions are given, with modifications for both Dirichlet boundary conditions and Neumann boundary conditions. An algorithm for computing the Galerkin coarse grid approximation is given. 1 Introduction In multigrid methods one needs discrete approximations of the differential equations to be solved not only on the given grid but also on coarser grids. There are two ways to obtain discrete approximations on coarser grids: discretization coarse grid approximation (DCA) and Galerkin coarse grid approximation (GCA). In DCA, the discrete system on each coarse grid is obtained in exactly the same way as on the finest grid, namely by discretizing the partial differential equations. In GCA, the discrete systems on coarse grids are computed algebraically, util..