A NEW FINITE-ELEMENT FORMULATION FOR CONVECTION-DIFFUSION PROBLEMS

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Abstract
A general numerical method for convection-diffusion problems is presented. The method is formulated for two-dimensional problems, but its key Ideas can be extended to three-dimensional problems. The calculation domain is first divided into three-node triangular elements, and then polygonal control volumes are constructed by joining the centroids of the elements to the midpoints of the corresponding sides. In each element, the dependent variable is interpolated exponentially in the direction of the element-average velocity vector and linearly in the direction normal to it. These interpolation functions respond to an element Peclet number and become linear when it approaches zero. The discretization equations are obtained by deriving algebraic approximations to integral conservation equations applied to the polygonal control volumes. The proposed method has the conservative property, can handle problems in the whole range of Peclet numbers, and avoids the false-diffusion difficulties that commonly afflict other methods. It has been successfully applied to a number of test problems.

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