Theoretical analysis of the worthiness of Henry and Elder problems as benchmarks of density-dependent groundwater flow models M.J. Simpson a , T.P. Clement a,b, * a Centre for Water Research, Department of Environmental Engineering, The University of Western Australia, Nedlands, 6907 Australia b Department of Civil Engineering, Auburn University, Auburn, AL 36830, USA Received 12 February 2002; received in revised form 18 June 2002; accepted 23 August 2002 Abstract 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. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Groundwater-modeling; Density-dependent flow; Unsaturated flow; Contaminant transport 1. Introduction Benchmarking the performance of a numerical code against standard analytical solutions is the necessary first step in testing the correctness of the numerical ap- proximations. The next logical step in the benchmarking process is testing the code to either reflect a laboratory- scale experimental data set or a field-scale case study. Completing these two benchmarking steps for a density- dependent flow model is a difficult task because the availability of analytical solutions or standard labora- tory/field data sets for the density-dependent flow problem is limited [31]. This contrasts with those prob- lems involving linear solute transport and/or density invariant groundwater flow, for which there exists sev- eral well known analytical and laboratory solutions to the governing equations [1,17]. In the literature there has been much discussion concerning the philosophy of the model benchmarking processes. While it is not the purpose of this communi- cation to enter into this philosophical discussion, the inherent problems with model verification should be acknowledged. Konikow and Bredeheoft [20] and Oreskes et al. [24] argue that verification and validation of numerical models of natural systems is impossible, as true natural systems are not closed and numerical results are always non-unique. While the importance of this argument should not be understated, the recognition of these philosophical issues should not detract from the need for accurate model development and testing, as the process of mathematical modeling is one of the useful options available for gaining insight into complex nat- ural systems. Konikow and Bredeheoft [21] suggested that a simple acknowledgement by the groundwater modeling com- munity might circumvent some of the philosophical is- sues associated with model validation and verification. * Corresponding author. Tel.: +1-334-844-6268; fax: +1-334-844- 6290. E-mail addresses: simpson@cwr.uwa.edu.au (M.J. Simpson), clem- ent@eng.auburn.edu (T.P. Clement). 0309-1708/03/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0309-1708(02)00085-4 Advances in Water Resources 26 (2003) 17–31 www.elsevier.com/locate/advwatres