SWIFT2D uses an alternating-direction implicit (ADI) method and a space- and time-staggered grid to solve the governing equations, such that each surface-water timestep is divided into two half timesteps-one half timestep for flow and transport in the x-direction and the other for the y-direction. In each of the two phases of the ADI method, the continuity equation and one of the components of the momentum equations are solved with local storage (and corresponding transport term of the continuity equation), local acceleration, pressure gradient, and the frictional term of the momentum equation treated implicitly. The last three terms on the left-hand side of Eq. 1 (the source and sink terms) are not included in the finite-difference solution, but are separately added to, or subtracted from, the cell volume. SEAWAT uses an implicit finite-difference approximation to solve the ground-water flow equation (Eq. (6)), and contains several alternative methods for solving the solute-transport equation (Eq. (7)), including implicit and explicit finite-difference methods with various weighting options and the method of characteristics.

The integrated code for SWIFT2D and SEAWAT requires cells that coincide and are identical in size. The integrated code was designed such that the domains of the two models need not be identical, provided that leakage fluxes can be neglected in areas where the two models do not overlap. Although not used for the Everglades application, this feature may prove useful for certain applications where the extension of the model domain is necessary in only one of the two systems.