Multiscale-finite-element-based ensemble Kalman filter for large-scale groundwater flow

In this paper, we propose an ensemble Kalman filter based on the mutiscale finite element method for the large-scale groundwater problem. The multiscale finite element method is employed to avoid the conventional fine-scale simulation during the forward prediction. The EnKF and the multiscale algorithm are integrated as independent components. They are connected by two modules: one for recovering the fine-scale information and the other for reconstructing the coarse-scale basis functions. The first module interpolates the coarse-scale solution with coarse-scale basis functions. Then the state covariance on the fine-scale mesh is obtained with less computational burden. The second module reconstructs coarse-scale basis functions when the model states have been updated. The proposed method is examined by synthetic cases. The results show that the proposed method with an appropriate coarsening level is able to produce satisfactory estimations for the conductivity field and history matching. The new method offers superior computational efficiency and significant saving in the computer memory.