Theoretical analysis of the worthiness of Henry and Elder problems as benchmarks of density-dependent groundwater flow models

Computer models must be tested to ensure that the mathematical statements and solution schemes accurately represent the physical processes of interest. Because the availability of benchmark problems for testing density-dependent groundwater models is limited, one should be careful in using these problems appropriately. Details of a Galerkin finite-element model for the simulation of density-dependent, variably saturated flow processes are presented here. The model is tested using the Henry salt-water intrusion problem and Elder salt convection problem. The quality of these benchmark problems is then evaluated by solving the problems in the standard density-coupled mode and in a new density-uncoupled mode. The differences between the solutions indicate that the Henry salt-water intrusion problem has limited usefulness in benchmarking density-dependent flow models because the internal flow dynamics are largely determined by the boundary forcing. Alternatively, the Elder salt-convection problem is more suited to the model testing process because the flow patterns are completely determined by the internal balance of pressure and gravity forces.