Different modelings of cell‐face velocities and their effects on the pressure–velocity coupling, accuracy and convergence of solution

Abstract

AbstractIn 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.