Application of multiscale finite element method in the uncertainty qualification of large-scale groundwater flow

In this article, we discuss the application of multiscale finite element method (MsFEM) to groundwater flow in heterogeneous porous media. We investigate the ability of MsFEM in qualifying the flow uncertainty. Monte Carlo simulation is employed to implement the stochastic analysis, and MsFEM is used to avoid a full resolution to the spatial variable conductivity field. Large-scale flow with high variability is investigated by inspecting the single realization as well as the probability distribution functions of head and velocity. The numerical results show that the performance of MsFEM depends on the ratio between the correlation length and the coarse element size. An accurate prediction to the velocity requires a much lower ratio than the head. The MsFEM has different convergence rates for the head and the velocity, while the convergence rates do not deteriorate as the variance grows.