Comparison of different numerical models using a two-dimensional density-driven benchmark of a freshwater lens

The physical experiment of Stoeckl and Houben (2012)* was taken as a benchmark to compare results of calculations by several finite volume and finite element programs. In the experiment, an acrylic glass box was used to simulate a cross section of an infinite strip island. Degassed salt water (density 1021 kg m-3) was injected, saturating the sand from bottom to top. Fluorescent tracer dyes (uranine, eosine and indigotine) were used to mark infiltrating fresh water (density 997 kg m-3) from the top. While freshwater constantly infiltrated, saltwater was displaced and a freshwater lens started to develop until reaching equilibrium. The experiment was recorded and analyzed using fast motion mode. The numerical groundwater flow models used for comparison are Feflow, Spring, OpenGeoSys, d3f and HydroGeoSphere. All programs are capable to solve the partial differential equations of coupled flow and transport. To ensure highest level of comparison, the setups are defined as similar as possible: identical temporal and spatial resolutions are applied to all models (triangular grid with 14,432 elements and constant time steps of 8.64 s); furthermore, the same boundary conditions and parameters are used; finally, the output of each model is converted into the same format and post-processed in the open-source program ParaView. Transient as well as steady state flow fields and concentration distributions are compared. Capabilities of the different models are described, showing differences, limitations and advantages. The results show, that all models are capable to represent the benchmark to a high degree. Still, differences are observed, even by keeping the models as similar as possible. Some deviations may be explained by omitted processes, which cannot be represented in certain models, whereas other deviations may be explained by program-specific differences in solving the partial differential equations. * Stoeckl, L., Houben, G. (2012): Flow dynamics and age stratification of freshwater lenses: experiments and modeling. J. Hydrol., 21 (458-459), pp. 9-15.