On the use of vorticity-vector-potential with a spectral tau method in rotating annular domains

Abstract

A new approach for the resolution of three-dimensional Navier-Stokes and energy equations is presented, using the vorticity-vector-potential formulation for multiply connected domains. The dependent variables are solved in a complex form to uncouple the equations in radial and azimuthal directions. A spectral tau method, with Chebyshev polynomials in radial and axial directions and Fourier series in the azimuthal one, is proposed for the prediction of flow structures and heat transfer of a Boussinesq fluid inside rotating annular domains. The integration in time utilizes a combination of second-order backward Euler and Adams-Bashforth schemes. The first results concern the stokes problem.