A discrete vector potential model for unsteady incompressible viscous flows

Abstract

A recent approach to generate a zero divergence velocity field by operating directly on the discretized Navier-Stokes equations is used to obtain the decoupling of the pressure from the velocity field. By following the methodology suggested by Amit, Hall, and Porsching the feasibility of treating three dimensional flows and multiply connected domains is analyzed. The present model keeps the main features of the classical vector potential method in that it generates a divergence-free velocity field through an algebraic manipulation of the discrete equations. At the same time the boundary conditions are still imposed on the discrete values of the primitive variables. The accuracy of the method is tested against the exact solution for a recirculating unsteady flow both in simply and doubly connected domains. Several applications to flow fields in three-dimensional enclosures or in multiply connected domains are presented and discussed in terms of accuracy and efficiency of the method.