Open Access

ARTICLE

A Parallel Multi-block Method for the Unsteady Vorticity-velocity Equations

by A. Grimaldi¹, G. Pascazio², M. Napolitano³

1 DIMeG & CEMeC, Politecnico di Bari, via Re David 200, 70125 Bari, Italy, e-mail: an.grimaldi@poliba.it.
2 DIMeG & CEMeC, Politecnico di Bari, via Re David 200, 70125 Bari, Italy, e-mail: pascazio@poliba.it.
3 DIMeG & CEMeC, Politecnico di Bari, via Re David 200, 70125 Bari, Italy, e-mail: napolita@poliba.it.

Computer Modeling in Engineering & Sciences 2006, 14(1), 45-56. https://doi.org/10.3970/cmes.2006.014.045

Abstract

This paper provides a numerical method for solving two- and three-dimensional unsteady incompressible flows. The vorticity-velocity formulation of the Navier--Stokes equations is considered, employing the vorticity transport equation and a second-order Poisson equation for the velocity. Second-order-accurate centred finite differences on a staggered grid are used for the space discretization. The vorticity equation is discretized in time using a fully implicit three-level scheme. At each physical time level, a dual-time stepping technique is used to solve the coupled system of non linear algebraic equations by various efficient relaxation schemes. Steady flows are computed by dropping the physical time derivative and converging the pseudo-time-dependent problem. A domain decomposition of the physical space is also employed: the multi-block algorithm allows one to handle multiply-connected domains and complex configurations and, more importantly, to solve each grid-block on a single processor of a parallel platform. The accuracy and efficiency of the proposed methodology is demonstrated by solving well known two-dimensional flow problems. Then, the steady and unsteady flows inside a cubic cavity are considered and the numerical results are compared with experimental and numerical data.

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