3-D finite element transport models by upwind preconditioned conjugate gradients

The CG schemes ORTHOMIN(k), GCR(k) and MR properly preconditioned appear to be robust, reliable and efficient solvers in the finite element integration of the diffusion-convection equation over 3-D subsurface systems. They allow for the easy treatment of a large number of nodes, i.e. for an effective limitation of the numerical dispersion through the control of the magnitude of the Peclet and Courant numbers. Upwinding helps improve considerably the performance of the solvers. CGR(k) turns out to be the most robust one while MR is the most economical in the vast majority of applications. If the Peclet and Courant numbers are not too far from the stability limits, MR is preferred. Upwinding allows for convergence also in critical strong convection-dominated cases when the Galerkin approach fails to converge. However it tends to increase the artificial dispersion and hence it must be managed with some care.