Level Set Method with Reinitialization for Interface Monitoring of Saltwater Intrusion Concerns with Some Applications

Abstract

This study examines the level set method with reinitialization (LSMR) for monitoring the interface in saltwater intrusion problems. The governing equations consist of a parabolic equation modeling groundwater flow and a hyperbolic equation (the level set equation) that tracks the evolution of the freshwater/saltwater interface. The level set equation used for interface tracking is based on the sharp-interface approach, wherein a regular scalar function is defined across the interface using the level set method. The weighted essentially non-oscillatory scheme and a third-order total variation diminishing Runge-Kutta scheme are used to solve the nonlinear partial differential equations governing flow, minimizing mass loss. These schemes are implemented in MATLAB. Numerical simulations for Glover’s problem, the Madras aquifer, and the Kawatani problem demonstrate that the results of the LSMR model closely align with those reported by other researchers. The study highlights that significant saltwater intrusion remains a major concern for coastal aquifers, which play a crucial role in supplying water for domestic, industrial, and agricultural needs. Accurate tracking of the sharp interface is essential to mitigate potentially harmful consequences.