STREAMLINE UPWIND SCHEME FOR CONTROL-VOLUME FINITE ELEMENTS, PART I. FORMULATIONS

Abstract

The basic features of the Galerkin and control-volume-based finite-element approximations are outlined. For convection-diffusion problems, these approximations could lead to unstable solutions. The streamline upwind Petrov Galerkin (SUPG) finite-element approach to overcome this problem is discussed. After this, extensions of the concepts in the SUPG approach are made to the control-volume-based finite-element method. The resulting streamline upwind control-volume (SUCV) finite-element method exhibits upwinding features similar to the SUPG method while retaining the conservative property of control-volume methods.