INVARIANT DISCRETIZATION OF THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS IN BOUNDARY FITTED COORDINATES

The discretization of the incompressible Navier-Stokes equation on boundary-fitted curvilinear grids is considered. The discretization is based on a staggered grid arrangement and the Navier-Stokes equations in tensor formulation including Christoffel symbols. It is shown that discretization accuracy is much enhanced by choosing the velocity variables in a special way. The time-dependent equations are solved by a pressure-correction method in combination with a GMRES method. Special attention is paid to the discretization of several types of boundary conditions. It is shown that fairly non-smooth grids may be used using our approach.