A frontal method based solution of the quasi‐three‐dimensional finite element model for interconnected aquifer systems. Steady and unsteady equations, with the E.N.S. method for fluid mass balance evaluation

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Abstract
The quasi‐three‐dimensional equations controlling the groundwater flow in heterogeneous and interconnected aquifer systems are discretized by finite elements, considering also the aquifer branching. A new method for fluid mass balance evaluation based on the equivalent nodal source (E.N.S.) concept allows one to express the balance in conservative terms, and interpret finite element equations as nodal balance equations. The solution of the system is based on the frontal method. Use of substructures limits the frontal increase in correspondence to the aquifer branching. In the steady state, the frontal method is integrated with an iterative solution technique to eliminate the frontal increase caused by the presence of aquitards. It converges very rapidly, using a forcing technique with an automatic parameter definition. In the unsteady case the same scope is achieved using a predictor‐corrector procedure which employs the Crank‐Nicolson method in the corrector phase.This very stable procedure permits use of fairly long time‐steps and concerns the case of source terms depending on piezometry (problem of interaction between water table and river). This method has been tested with several fairly complex cases.