The saltpool benchmark problem – numerical simulation of saltwater upconing in a porous medium

Recently, a series of laboratory experiments was carried out in which a typical variable-density flow problem in a porous medium was investigated. A stable layering of saltwater below freshwater is affected by the recharge and discharge of freshwater on the top. The experiments were conducted with 1% and 10% initial salt-mass fraction contrasts. In this paper, we define a mathematical model problem, which is able to reproduce the experimental results within a reasonable accuracy. To this end, the sensitivity of the model with respect to model parameters is investigated. An inverse modelling leads to an appropriate choice of the model parameters and the definition of the mathematical benchmark problem. It will become clear that, in the 10% case, the transversal dispersion coefficient plays an important role. Detailed numerical investigations are carried out and reference solutions are obtained. For the high concentration case a very high spatial grid resolution using up to 16 million grid points is necessary. Error bounds are derived for the solutions without any a priori assumption on regularity and convergence.