A parallel multi-block method for the unsteady 3D vorticity-velocity Navier-Stokes equations

This paper provides an efficient and accurate numerical method for solving two- and three-dimensional unsteady incompressible flows. The vorticity-velocity formulation of the Navier-Stokes equations is considered, with a transport equation for the vorticity and a second-order Poisson equation for the velocity. Second-order centred finite differences on a staggered grid are employed for the space discretization. The vorticity equation is discretized in time using a fully implicit three level scheme coupled with the velocity vector equation and the resulting system is solved by a dual-time stepping technique employing very efficient relaxation schemes. A domain decomposition of the physical space is also employed. The multi-block algorithm allows to handle multiply-connected domains and complex configurations and, more importantly, a straightforward parallelization of the code by solving each grid-block on a single processor. The accuracy and efficiency of the proposed methodology is demonstrated by solving well known two-dimensional flow problems. Then, numerical solutions of the steady and unsteady flows inside a cubic cavity is considered and the results are compared with experimental and numerical data.