EVALUATION AND ENHANCEMENTS OF SOME CONTROL VOLUME FINITE-ELEMENT METHODS—PART 2. INCOMPRESSIBLE FLUID FLOW PROBLEMS

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Abstract
This is the second of two companion papers dealing with the evaluation and enhancements of some control volume finite-element methods (CVFEMs) for fluid flow and heat transfer. One unequal-order CVFEM and two versions of an equal-order CVFEM, for the prediction of two-dimensional incompressible fluid flow are examined in this paper. In the unequal-order CVFEM, six-node macroelements and three-node subelements are used to discretize the calculation domain, and the velocity components are interpolated by flow-oriented upwind-type functions. In the equal-order CVFEM, the calculation domain is discretized by three-node triangular elements, the dependent variables are colocated, and the velocity components are interpolated by flow-oriented upwind-type functions which explicitly account for the influence of the pressure gradient on the velocity distribution in each element. The SIMPLEC procedure is used to solve the discretized equations in all three CVFEMs. The proposed equal-order CVFEM is more accurate than the unequal-order CVFEM, however, it requires much more CPU time to achieve converged solutions, due to the type of equations which arise in the proposed solution algorithm. This difficulty may be alleviated by implementing the equal-order method in conjunction with solution algorithms other than SIMPLEC.