Every MODFLOW model must include one and only one of the solver packages. Six different solvers have been incorporated into MODFLOW-2000. However, because of licensing restrictions, one of them, LMG, is not included in the publicly distributed version of MODFLOW.
The PCG solver is very widely used. However, for large steady-state models, the multi-grid solvers, GMG or LMG, may be preferable because they can be faster and in some cases they can reach a satisfactory solution when other solvers do not. For transient models, the multi-grid solvers can be slower than the PCG solver. The PCGN package provides additional means by which the solution of nonlinear ground-water flow problems can be controlled as compared to existing solver packages for MODFLOW. The NWT solver is only available in MODFLOW-NWT.
SOR (not included in MODFLOW-2005 or MODFLOW-LGR).
Each solver has convergence criteria that control when the model solution is considered adequate. Often the model will look at the percent discrepancy in the water budget to determine whether the solver criteria have been set strictly enough. If the percent discrepancy is less than 1%, this is often considered adequate. However, the rule can fail; Ahlfeld and Hoque (2008) report a case where a model with a percent discrepancy in the water budget of 0.012% was not sufficiently accurate for its intended purpose. Modelers are advised to investigate how varying the solver parameters affects the predictions of interest in the model rather than relying solely on the percent discrepancy in judging the adequacy of the model.
Ahlfeld, D.P., and Hoque, Y, 2008. Impart of Simulation Model Sover Performance on Ground Water Management Problems. Groundwater, 46(5), p. 716-726.