Lattice Boltzmann Method in Saltwater Intrusion Modeling

This study develops a saltwater intrusion simulation model using a lattice Boltzmann method (LBM) in a two-dimensional coastal confined aquifer. The saltwater intrusion phenomenon is described by density-varied groundwater flow and mass transport equations, where a freshwater-saltwater mixing zone is considered. Although primarily developed using the mesoscopic approach to solve macroscopic fluid dynamic problems, e.g., Navier-Stoke equation, LBM is able to be adopted to solve physical-based diffusion-type governing equations as for the groundwater flow and mass transport equations. In this study, the density-varied groundwater flow equation and the advection-dispersion equation (ADE) are modeled by the lattice Boltzmann method. Under the consideration on the steady-state groundwater flow due to low storativity, in each time step the flow problem is modified to be a Poisson equation and solved by LBM. Nevertheless, the groundwater flow is still a time-marching problem with spatial-temporal variation in salinity concentration as well as density. The Henry problem is used to compare the LBM results against the Henry solution.