Discrete Exterior Calculus Method for Groundwater Flow Modeling

Abstract

A numerical formula for modeling groundwater flow is presented in this study, derived from the principles of discrete exterior calculus (DEC). The study begins with transforming the governing equations for unsteady flow into formulas in the framework of exterior calculus, utilizing differential forms and their operators. The spatial discretization of the exterior calculus formula is based on the conception of simplicial complex and its dual mesh, while the time derivative term is discretized using the difference numerical scheme. Following the above discretization scheme, a mixed numerical formulation was developed, with flux and pressure as primary variables. To evaluate the DEC-based method’s effectiveness and accuracy in modeling groundwater flow, an extensive numerical study is conducted. The assessment includes comparisons with analytical solutions, such as Theis’s solution for a single well, as well as numerical results obtained from simulating multi-well pumping scenarios using established methods. The solutions exhibit a high degree of consistency with both analytical and numerical results. Furthermore, the results demonstrate the applicability of the proposed approach in more complex settings, ranging from pit dewatering with a waterproof curtain to three-dimensional flow with cutoff barriers. The results illustrate the potential of the DEC method as an effective groundwater solver, distinguished by its excellent local mass conservation.