A modified multiscale finite element method for well-driven flow problems in heterogeneous porous media

In this paper we propose a modified multiscale finite element method for solving the well-driven groundwater flow problems with heterogeneous coefficients defined on a fine scale. The key idea of the method is to use the fine-scale solution of local well-driven flow problems subject to generic boundary conditions to determine the boundary conditions of the multiscale base functions in the near-well region. As a consequence, these base functions are adapted not only to the local properties of the hydraulic parameter but also to the local variations of the pressure field in the well vicinity. Numerical experiments with a random lognormal hydraulic conductivity field are carried out for both steady and transient groundwater flow problems driven by pumping well. The numerical results show that the modified approach provides considerably more accurate coarse-scale simulations for well-driven groundwater flow, relative to reference fine-scale results, than does the standard multiscale finite element method.