The flow-condition-based interpolation (FCBI) finite element procedure is improved for the solution of two-dimensional advection-diffusion problems. Novel numerical schemes are developed by introducing, in one scheme, the link-cutting bubbles [1] and, in another scheme, the general solution of the advection-diffusion equation into the trial functions for the advection term. In the proposed algorithms, as in the conventional FCBI procedure [2,3], no artificial parameters are included to reach stability for high Peclet number flow. The governing equation is discretized by employing a Petrov-Galerkin formulation, in which step functions are used as weight functions to satisfy local flux conservation in selected control volumes of the finite element discretization. Similarities and relations among the FCBI procedure, the link-cutting bubbles and the streamline-upwind Petrov-Galerkin (SUPG) formulations [4] are established considering the solution of the one-dimensional advection-diffusion problem. Then, the proposed numerical schemes are applied to two-dimensional thermal flows over a square domain. Various problems are considered with various mesh topologies. In this way the capabilities and the effectiveness of the new methods are identified and demonstrated for a wide range of Peclet numbers. The research accomplishments will be published in a full paper [5].
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