Experimental and computational validation and verification of the Stokes–Darcy and continuum pipe flow models for karst aquifers with dual porosity structure

Abstract

AbstractIn our previous study, we developed the Stokes–Darcy (SD) model was developed for flow in a karst aquifer with a conduit bedded in matrix, and the Beavers–Joseph (BJ) condition was used to describe the matrix–conduit interface. We also studied the mathematical well‐posedness of a coupled continuum pipe flow (CCPF) model as well as convergence rates of its finite element approximation. In this study, to compare the SD model with the CCPF model, we used numerical analyses to validate finite element discretisation methods for the two models. Using computational experiments, simulation codes implementing the finite element discretisations are then verified. Further model validation studies are based on the results of laboratory experiments. Comparing the results of computer simulations and experiments, we concluded that the SD model with the Beavers–Joseph interface condition is a valid model for conduit–matrix systems. On the other hand, the CCPF model with the value of the exchange parameter chosen within the range suggested in the literature perhaps does not result in good agreement with experimental observations. We then examined the sensitivity of the CCPF model with respect to the exchange parameter, concluding that, as has previously been noted, the model is highly sensitive for small values of the exchange parameter. However, for larger values, the model becomes less sensitive and, more important, also produces results that are in better agreement with experimental observations. This suggests that the CCPF model may also produce accurate simulation results, if one chooses larger values of the exchange parameter than those suggested in the literature. Copyright © 2011 John Wiley & Sons, Ltd.