Upwind preconditioned conjugate gradients for finite element transport models

The iterative weighted residual solution of diffusive-convective equations may easily fall to converge in convection-dominated models. If the classical Galerkin approach is used, oscillations may also occur. To cope with this problem, an upwind weighting technique may prove appropriate. In the present paper an upwind finite element model is developed to analyze the 2-D transport of subsurface contaminants and is solved by preconditioned generalized conjugate residual schemes (GCR) especially designed for unsymmetric matrices. Three different algorithms, the ORTHOMIN(k), the GCR(k), and the Minimal Residual are compared on test problems whose size is up to 1500 for a wide range of Peclet and Courant numbers. The numerical results show that these numerical schemes are all robust, efficient, and reliable. The performace of the Minimal Residual is usually better, and particularly so for lage-sized problems.