Improvement of generalized finite difference method for stochastic subsurface flow modeling

Uncertainty is embedded in groundwater flow modeling because of the heterogeneity of hydraulic conductivity and the scarcity of measurements. To quantify the uncertainty of the modeled hydraulic head, this study proposes an improved version of the meshless generalized finite difference method (GFDM) for solving the statistical moment equation (ME). The proposed GFDM adopts a new support sub-domain for calculating the derivative of the head to improve accuracy. Synthetic fields are applied to validate the proposed method. The proposed GFDM outperforms the conventional GFDM in terms of accuracy based on a comparison with the results of the finite difference method. The ME-GFDM scheme is shown to be 2.6 times faster than Monte Carlo simulation with comparable accuracy. The ME-GFDM is versatile in that it easily handles irregular domains, allows the node location and number to be changed, and allows the sequential addition of new data without remeshing, which is required for traditional mesh-based methods.