INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2011; 65:969–988 Published online 12 January 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/fld.2224 Different modelings of cell-face velocities and their effects on the pressure–velocity coupling, accuracy and convergence of solution H. Alisadeghi 1,2,‡ and S. M. H. Karimian 1,2,∗, †, § 1 Department of Aerospace Engineering, Amirkabir University of Technology, P.O. Box 15875-4413, Tehran, Iran 2 Center of Excellence in Computational Aerospace Engineering, Iran SUMMARY In this article, a detailed study on the effects of different modelings of cell-face velocities on pressure– velocity coupling, accuracy and convergence rate of the solution has been conducted. Discussions are focused on the collocated scheme of Schneider and Karimian (Computational Mechanics 1994; 14: 1–16) in the context of a control-volume finite-element Method. In this scheme, variables at the control volume surface are evaluated based on the physics of their governing equations, and the fully coupled system obtained is solved using a direct sparse solver. A special test problem has been defined to check the pressure–velocity coupling for all of the formulations. Other test cases, including Taylor problem, inviscid converging–diverging nozzle and the lid-driven cavity, have been conducted for different Reynolds numbers, mesh sizes and time steps to investigate the accuracy and the performance of the formulations. Finally, a reliable and efficient scheme for the evaluation of cell-face velocities is proposed, which can be easily extended to three dimensions. Copyright 2010 John Wiley & Sons, Ltd. Received 12 May 2009; Revised 3 September 2009; Accepted 8 September 2009 KEY WORDS: incompressible flow; control-volume-based finite element; pressure-based algorithm; collocated grid; primitive variable; cell-face velocity 1. INTRODUCTION For more than three decades, numerical solution of the incompressible Navier–Stokes (INS) equa- tions has been a subject of interest to engineers and researchers. During this period, numerical methods have faced two main difficulties. The first difficulty is due to non-linearity and improper modeling of the convective term. For example, in high-Reynolds number flows where a careful treatment of the convective term is important, the inattention to physics of flow may produce spurious oscillations in the solution, which in some cases results in the convergence failure. To overcome this difficulty, different techniques have been proposed in the literature. The first- and second-order upwind schemes [1, 2], hybrid scheme [3, 4] and QUICK method [5], and also Physical Influence Schemes (PIS) [6–11] are some of them. The second difficulty in solving INS equations is the pressure–velocity decoupling. This problem arises from the fact that the continuity equation does not involve the pressure variable directly. This causes, on the one hand, difficulties in the segregated solution of governing equations and on the other hand, generation of non-physical oscillations in pressure and velocity fields. These oscillations often referred to ∗ Correspondence to: S. M. H. Karimian, Department of Aerospace Engineering, Amirkabir University of Technology, P.O. Box 15875-4413, Tehran, Iran. † E-mail: hkarim@aut.ac.ir ‡ PhD Candidate. § Professor. Copyright 2010 John Wiley & Sons, Ltd.