An efficient model for solving density driven groundwater flow problems based on the network simulation method

The Henry and Elder problems are once more numerically studied using an efficient model based on the Network Simulation Method, which takes advantage of the powerful algorithms implemented in modern circuit simulation software. The network model of the volume element, which is directly deduced from the finite-difference differential equations of the spatially discretized governing equations, under the streamfunction formulation, is electrically connected to adjacent networks to conform the whole model of the medium to which the boundary conditions are added using adequate electrical devices. Coupling between equations is directly implemented in the model. Very few, simple rules are needed to design the model, which is run in a circuit simulation code to obtain the results with no added mathematical manipulations. Different versions of the Henry problem, as well as the Elder problem, are simulated and the solutions are successfully compared with the analytical and numerical solutions of other authors or codes. A grid convergence study for the Henry problem was also carried out to determine the grid size with negligible numerical dispersion, while a similar study was carried out with the Elder problem in order to compare the patterns of the solution with those of other authors. Computing times are relatively small for this kind of problem.