Probabilistic collocation method for unconfined flow in heterogeneous media

In this study, we make use of the probabilistic collocation method in studying nonlinear flow in heterogeneous unconfined aquifers. In realistic problems there may exist multiple random inputs, nonlinearity, rainfall/evaporation, wells, nonstationary trends and complex boundary conditions. These complications may lead to strong spatial nonstationarity in the flow, which cannot be handled well with most existing approaches. In the present work, a general unconfined problem is explored with the probabilistic collocation method. The stochastic differential equation of flow is reduced into a set of deterministic equations that can be solved with the aid of existing deterministic solvers without any modification. Two types of random inputs are considered, which may be either perfectly correlated or uncorrelated. This approach is demonstrated through some synthetic cases in the presence of rainfall/evaporation, pumping/injection wells, composite mean conductivity fields. The approach can easily combine the proven techniques in deterministic simulations with stochastic treatments and thus provides a practical way for solving stochastic problems with complex fields of hydraulic parameters, nontrivial boundary conditions, and realistic sources/sinks.