Abstract
This is the first of two companion papers dealing with the evaluation and enhancements of some control volume finite-element methods (CVFEMs) for fluid flow and heat transfer. This paper examines three CVFEMs for two-dimensional convection-diffusion problems. In the first CVFEM, the scalar dependent variable is interpolated by a flow-oriented upwind type function which does not explicitly account for the influence of source terms. In the second CVFEM, the interpolation function employs flow-oriented upwinding and, in addition, includes a flow-oriented term which explicitly accounts for the influence of sources. The third CVFEM represents an attempt to enhance the performance of the first and second CVFEMs. The interpolation function used in the third CVFEM employs flow-oriented upwinding and includes terms which explicitly account for the influence of sources in directions both parallel and normal to the flow. It was found that significant improvements in the accuracy of the solutions can often be obtained when a source-related term is included in the interpolation function. The proper choice of this source-related term, however, depends on the nature of the problem being solved.
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