Solution of three-dimensional groundwater flow equations using the strongly implicit procedure

Abstract A three-dimensional numerical model has been coded to use the strongly implicit procedure for solving the finite-difference approximations to the ground-water flow equation. The model allows for: (1) the representation of each aquifer and each confining bed by several layers; and (2) the use of an anisotropic hydraulic conductivity at each finite-difference block. The model is compared with a previously developed quasi-three-dimensional model by simulating the steady-state flow in an aquifer system in the Piceance Creek Basin, Colorado. The aquifer system consists of two aquifers separated by a leaky confining bed. The upper aquifer receives recharge from precipitation and is hydraulically connected to streams. For this problem, in order to make a valid comparison of results, a single layer was used to represent each aquifer. Furthermore, the need for a layer to represent the confining bed was eliminated by incorporating the effects of vertical leakage into the vertical component of the anisotropic hydraulic conductivity of the adjacent aquifers. Thus, the problem was represented by only two layers in each model with a total of about 2,100 equations. This restricted the effects of flow in the confining layer to the vertical component, but simulations with a third layer in the three-dimensional model permitting horizontal flow in the confining bed show that the two-layer approach is reasonable. Convergence to a solution of this problem takes about one minute of computer time on the IBM/155. This is about 30 times faster than the time required using the quasi-three-dimensional model.