ON THE USE OF THE ELDER (1967) CONVECTION EXPERIMENT AS A BENCHMARK PROBLEM FOR VARIABLE-DENSITY TRANSPORT MODELS

Typically, variable-density transport models are tested by comparing model output with results of well-defined scenarios, or benchmark problems. A widely used test case is the Elder (1967) problem of free thermal convection. A model is believed to be satisfactorily validated if visual inspection indicates that simulated isochlor distributions reproduce those previously published. However, numerous authors have presented Elder results that are qualitatively different and yet physically correct. Therefore, in order to quantitatively characterize the Elder problem, a number of indicators have recently been introduced that are not prone to subjectivity of visual inspection. The indicators have been retrieved by simulating the Elder experiment with the SUTRA model; they are not experimentally measured nor are they compared with the results from other numerical simulators. Therefore, it remains unknown whether quantitative indicators, obtained from a specific numerical code, can be used to benchmark the Elder problem.

To address this question, the HYDROSPHERE model, which solves 3D variably-saturated flow and solute transport in discretely-fractured porous media, has been modified to account for fluid density variations. It employs the control volume finite element method (CVFE), uses the equivalent freshwater head as flow parameter and linearly relates the fluid density with salinity. It was found that, with HYDROSPHERE, the quantitative indicators of the Elder problem could not be adequately reproduced. Consequently, the effect of using other flow variables (freshwater pressure head and fluid pressure) and different density-salinity relationships (linear, nonlinear) was studied and revealed a high sensitivity of the Elder results to these variables. In a further investigation, HYDROSPHERE results (isochlors) were compared with those obtained from a number of other numerical codes. It was discovered that the Elder results are highly sensitive to the numerical model used. A visual match of isochlors can only be achieved if both the model approach (CVFE) and the flow parameters of the two codes are identical. It was finally concluded that, in view of the great sensitivity of the Elder results, the Elder salt convection problem can not be used as a quantitative benchmark problem.