Numerical solutions to the incompressible Navier-Stokes equations : Finite difference solutions in curvilinear coordinates

A finite difference scheme for the incompressible Navier-Stokes equations in 2-dimensionalcurvilinear coordinates is derived. The scheme uses high-order Summation-By-Parts operatorsand boundaries are handled by the Projection method. Using the energy method, the scheme isproven stable and well-posed with Dirichlet boundary conditions for general curvilineartransforms. Numerical tests show convergence of the scheme for high-order operators on theTaylor-Green vortex problem using three different transformations. Furthermore, the Lid-drivencavity problem is tested and it shows that employing curvilinear transforms to create a densergrid near boundaries can achieve greater accuracy when observing boundary layer effects.