A Perspective on the numerical-Solution of Convection-dominated Transport Problems - a Price to Pay for the Easy Way Out

In a brief but fundamental review of the evolution of the conventional numerical techniques used in the solution of convection-dominated transport problems, we explore the difficulties that have been remedied to various degrees by various workers. In the course of this review we obtain the performance characteristic of the Crank-Nicolson Galerkin finite element method in the form of a curve in Peclet number and Courant number space. We show that the performance can be altered through a new upwind parameter that can easily be incorporated into many of the existing numerical solution methods. By providing an insight into the limitations of some of these methods we demonstrate, by means of numerical experiments, that the proposed upwinding procedure ensures acceptable solutions throughout the Pe-Cr space at a reasonable cost of the smearing effect.