The effect of choosing dependent variables and cell-face velocities on convergence of the SIMPLE algorithm using non-orthogonal grids

In this paper the effects of choosing dependent variables and cell face vel ocities on convergence of the SIMPLE algorithm are discussed. Using differe nt velocity components as either dependent variables or cell-face velocitie s, both convergent rate and calculation accuracy of the algorithm are compa red and studied. A novel method, named "cross-correction", is developed to improve the convergence of the algorithm of using non-orthogonal grids. Cas es with benchmark and analytical solutions are used for numerical experimen ts and validation. The results show that, although different velocity compo nents art, employed as either dependent variables or cell face velocities, there is no obvious difference in both the convergent rates and numerical s olutions. Moreover, the "cross-correction" method is validated by computati ons with several first-order and high-order convection schemes; and the gen erality of convergence improvement achieved by the method is shown in the p aper.