Regional Groundwater Flow Modeling Using Improved Isogeometric Analysis: Application and Implications in Unconfined Aquifer Systems

Isogeometric Analysis (IGA) employs B-Splines and Non-Uniform Rational B-Splines (NURBS) to construct approximating functions, establishing a numerical approach for solving governing differential equations related to elliptic diffusion. In this study, IGA is implemented to model groundwater flow in unconfined aquifer systems bearing different geometries. The proposed IGA methodology exploits its approximating functions to intricately delineate the problem's geometry, achieving this precision with a minimal set of control points. A novel boundary-updating formula is introduced, dynamically repositioning fundamental points within each iteration to enhance accuracy. The efficacy of the improved IGA is verified through four numerical and benchmark simulations, including comparisons with analytical solutions. The IGA-derived results outperform the analytical solutions and closely align with the predicted heads of groundwater at the specified nodes using known numerical solutions (with less than 5% difference). Using IGA offers several benefits over analytical solutions, including enhanced continuity of the approximation solution and improved precision. The present formulation enables efficient simulation of groundwater flow, considering the exact aquifer domain geometry, while only requiring a small number of degrees of freedom. This innovative approach holds the potential to significantly expedite model creation, particularly in intricate structural scenarios, as it obviates the need for intricate meshing and enables the simultaneous development of geometry and computational models.