Invariant discretization of the incompressible Navier‐Stokes equations in boundary fitted co‐ordinates

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.