The two-dimensional streamline upwind scheme for the convection-reaction equation

This paper is concerned with the development of the finite element method i n simulating scalar transport, governed by the convection-reaction (CR) equ ation. A feature of the proposed finite element model is its ability to pro vide nodally exact solutions in the one-dimensional case. Details of the de rivation of the upwind scheme on quadratic elements are given. Extension of the one-dimensional nodally exact scheme to the two-dimensional model equa tion involves the use of a streamline upwind operator. As the modified equa tions show in the four types of element, physically relevant discretization error terms are added to the flow direction and help stabilize the discret e system. The proposed method is referred to as the streamline upwind Petro v-Galerkin finite element model. This model has been validated against test problems that are amenable to analytical solutions. In addition to a funda mental study of the scheme, numerical results that demonstrate the validity of the method are presented. Copyright (C) 2001 John Wiley & Sons, Ltd.