This chapter includes a broad survey of numerical approaches for multiphase flow using classifications based on particle reference frame, relative velocity magnitude, and relative particle size to the grid size. These approaches are then considered for Brownian motion and turbulent diffusion. Throughout this chapter, comments are made on selecting the numerical approach for a given flow based on the approach’’s ability to capture physics and computational requirements (best tools for the job and costs).

Saltwater intrusion into coastal aquifers menace multiple coastal areas globally, degrading groundwater quality, which poses an important threat to freshwater supply for agricultural, industrial and domestic utilization. Groundwater over-exploitation used to be commonly recognized as the principle factor causing saltwater intrusion, while sea-level rise, intensified storm surges and precipitation change have grown to become important drivers of factors inducing saltwater intrusion as well. In the context of exacerbated human activities such as groundwater over-exploitation due to the ever-increasing water demand because of population growth and economic and social development, as well as sea-level rise and increased frequency and intensity of extreme weather events and warmer temperatures and changing precipitation patterns and regimes resulting from climate change, the phenomenon of saltwater intrusion worldwide has been seriously aggravated recently. A deeper understanding of the theories and multiple pathways of saltwater intrusion, the commonly-used methods to investigate the extent of saltwater intrusion, as well as numerical approaches to assess the impacts of anthropogenic activities and climate change on saltwater intrusion in future are of great importance to mitigate its negative effects.