Finite difference vorticity methods

Computations are presented for finite difference vorticity and primitive methods for the time dependent incompressible Navier Stokes equations in bounded domains. To directly compare solutions of the methods, modifications must be made to the primitive method and these are described. Both methods are based on semi-discrete methods that have been proven to be second order accurate. The computational results show second order uniform convergence in the velocities and vorticity using arbitrary (not compatible at time 0) initial data showing the validity of the time discrete methods for which only partial convergence results are known. An increase in the expected convergence order of the boundary vorticity using Thom's first order boundary condition is observed. Comparisons between the methods and between different boundary conditions in the vorticity method are given.