Simulation of vorticity dominated flows using a hybrid approach. I: Formulation

Abstract The formulation of a numerical solution method for the Navier–Stokes equations in domains with cylindrical boundaries based on a hybrid spectral – finite difference approach is presented. The main contributions of the present paper are complete proofs for the pole conditions for scalar and vector fields and the modified pdes for the streamfunction modes that are shown to possess solutions satisfying the pole conditions.