| Abstract: | A discretization scheme is presented which, unlike the standard higher-order finite difference and spline methods, does not give rise to unphysical solution modes and boundary conditions. Practical application of this scheme is achieved via the DCMG algorithm recently developed by the same author, which turns out to be able to find a converged solution of the ψ-ζ Navier-Stokes equations in about the same time for highorder as for low-order discretization schemes. Examples are presented for the driven cavity problem to explore the accuracy of the new method. Finally, a local analysis is performed of the corner singularities which exist in driven cavity flow, and their effect on the overall accuracy of the solutions obtained by polynomial interpolation methods is investigated. |
