Numerical solution of 3-D groundwater flow involving free boundaries by a fixed finite element method

Abstract

Groundwater flow in unconfined aquifers involves the determination of the free surface. Additionally, difficulties arise when dealing with seawater intrusion into unconfined aquifers, because this requires the location of both the phreatic surface and the interface separating freshwater from salt-water. A numerical procedure is developed for solving these problems in steady state with the finite element technique, assuming that groundwater flow is considered to occur only in the freshwater region of the saturated zone. The problem is solved with a fixed finite element mesh by iteratively adjusting the moving boundaries. This is achieved without explicitly changing the coefficient matrix of the finite element equations, which makes the method computationally fast. For the free surface problem, test examples demonstrate that the technique is accurate when compared to Polubarinova Kochina's analytical solution and laboratory measurements, and efficient when compared to the moving finite element mesh technique. For the saltwater intrusion interface, test problems, including saltwater intrusion into confined and unconfined aquifers, demonstrate that the technique is also accurate when compared to analytical solutions and laboratory measurements.