Relevance of solutions to the Navier-Stokes equations for explaining groundwater flow in fractured karst aquifers

We examine the use of numeric flow solutions of the Navier-Stokes (N-S) equations to improve flow modeling in fractured karst aquifers. The N-S equations were discretized with both the meshed finite difference method (FDM) and the meshless smoothed particle hydrodynamics method. The results using the FDM model were successfully compared with those taken from the literature. The N-S equations were solved numerically for two practical problems in karst aquifers: (a) the horizontal displacement of the saltwater/ freshwater sharp interface in fissures due to groundwater overexploitation and (b) the pressure and velocity profiles in fissures in the vicinity of an injection well. In the first problem, the numeric N-S solution suggests an exponential time advancement of the freshwater/saltwater interface in fissures. In the second problem, the unsteady water velocity and pressure profiles were determined in fissures having variable apertures in the vicinity of an injection well. The N-S simulation results agreed well with the data collected during the test, thereby removing any uncertainty in the estimation of the aquifer transmissivity.