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.
Bibliographical noteFunding Information:
The authors acknowledge the Army High Performance Computing Research Center (AHPCRC) at the University of Minnesota, the Minnesota Supercomputer Institute (MSI), and the Broken Hill Proprietary (BHP) Research and Technologies, Australia, for a research grant. The authors also thank Suhas V. Patankar and Henryk Stolarski of the University of Minnesota for useful discussions and input.