THE NUMERICAL TREATMENT OF ADVECTION: A PERFORMANCE COMPARISON OF CURRENT METHODS

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Abstract
A new “test problem ” for evaluating numerical models of advection is introduced, which exhibits many of the features encountered in practical advection-diffusion problems such as streamline curvature and steep variations in the advected variable. The problem was devised for the Third Meeting of the International Association for Hydraulic Research Working Group on Refined Modeling of Flow. At the meeting solutions of the problem generated by more than 20 different methods were reported. These methods are presented here and their relative performances compared and analyzed. No single method emerges as best, although some clearly perform better than others. It seems that advection modeling remains the art of compromise between diffusive and oscillatory errors.