Stream functions and equivalent freshwater heads for modeling regional flow of variable-density groundwater: 1. Review of theory and verification

Steady state flow of variable-density groundwater is simulated using equivalent freshwater heads and stream functions. On the basis of the work by De Josselin de Jong (1960,1969), fluids with different fluid densities are replaced by one hypothetical fluid, and singularities are introduced along interfaces where the actual fluids change densities. The basic flow equation describing variable-density flow, written in terms of equivalent freshwater head, is used to derive the corresponding stream function equation and associated boundary conditions. Neumann boundary conditions for the stream function equation can be determined from gradients of equivalent freshwater heads along the boundary. Stream functions provide a direct representation of the groundwater flow pattern and flow rates where fluid densities vary in space. In comparison, equivalent freshwater heads and fluid densities describe the two driving forces, hydraulic gradient and buoyancy force, but head gradients do not necessarily describe the flow direction of variable-density groundwater in isotropic media. Comparison of the finite element formulations indicates that potential errors in the centroid-consistent velocity calculation based on the stream function solution can be expected to be smaller than those in the velocity calculation based on the head solution for cross-sectional flow models, because discretization in the vertical direction is typically finer than in the horizontal direction.