A control volume finite‐element method for numerical simulating incompressible fluid flows without pressure correction

This paper presents a numerical model to study the laminar flows induced in confined spaces by natural convection. A control volume finite‐element method (CVFEM) with equal‐order meshing is employed to discretize the governing equations in the pressure–velocity formulation. In the proposed model, unknown variables are calculated in the same grid system using different specific interpolation functions without pressure correction. To manage memory storage requirements, a data storage format is developed for generated sparse banded matrices. The performance of various Krylov techniques, including Bi‐CGSTAB (Bi‐Conjugate Gradient STABilized) with an incomplete LU (ILU) factorization preconditioner is verified by applying it to three well‐known test problems. The results are compared to those of independent numerical or theoretical solutions in literature. The iterative computer procedure is improved by using a coupled strategy, which consists of solving simultaneously the momentum and the continuity equation transformed in a pressure equation. Results show that the strategy provides useful benefits with respect to both reduction of storage requirements and central processing unit runtime. Copyright © 2006 John Wiley & Sons, Ltd.