Improved Formulations of the Discretized Pressure Equation and Boundary Treatments in Co-Located Equal-Order Control-Volume Finite-Element Methods for Incompressible Fluid Flow

Improved formulations of the discretized pressure equation and boundary treatments in co-located, equal-order, control-volume finite-element methods for the prediction of incompressible fluid flow are presented in the context of steady, planar two-dimensional problems. Three-node triangles and polygonal-cross-section control volumes, created by joining element centroids to midpoints of the sides, are used. The proposed improvements maintain the strength of coefficients in the discretized pressure equations, and help in keeping them diagonally dominant. Thus they facilitate convergence of iterative solution methods and the results do not display physically untenable features. Solutions of two test problems are presented and discussed.