An Equal-Order Control-Volume Finite-Element Method for Fluid Flow in Arbitrary Triangulations

The control-volume finite-element method ( CVFEM), proposed by Baliga and Patankar, has been used with success to solve 2D fluid flow problems. It is based in a domain discretization into three-node triangular elements. It is shown here that the usual interpolating shape Junctions can be inadequate in elements with obtuse angles, leading to ill-conditioned matrices and very large solving times. A simple automatic procedure for anticipating such difficulties before the elementary matrix evaluation stage is proposed, A new interpolating Junction, devised for replacing the earlier one in obtuse elements, is also presented. The proposed CVFEM is proven to be faster and sturdier than the earlier one in grids with obtuse elements. It is, however, more diffusive in cases for which the earlier method is capable of giving a converged solution.