Numerical investigation of nonuniform free surface flows in heterogeneous porous media

One of the major problems of the fluid mechanics of porous media is the study of the consequences had by the heterogeneity of hydraulic conductivity on the flow field and on the transport processes. This work lies within this scope and in particular, investigates the case of unconfined aquifers, in which there is also the complication of nonuniform flow and of free surface. The preathic aquifer is a physical configuration which has great importance from a practical point of view (in fact it is quite often encountered within engineering and environmental contexts), and at the same time it brings important and interesting numerical problems. This work proposes a numerical study of the mathematical model (represented by a stochastic partial differential equation) through a Monte Carlo simulation coupling an algorithm for the generation of random gaussian fields to simulate porous media heterogeneity and the finite element method to solve the deterministic mathematical problem. The whole numerical algorithm is here presented and analysed. The results shown witness the importance of the problem and are immediately useful for engineering purposes.