Treatment on non-linear boundary conditions in groundwater modeling with Eigenvalue Methods

Abstract

Summary Mathematical models to evaluate water resources management should simultaneously consider surface and groundwater components as well as the hydraulic interaction between them. If we wish to take the stochastic behaviour of surface hydrology into account, scenarios over long time horizons should be defined. Therefore, groundwater flow models with low computational cost are required. In addition, a distributed aquifer model is required to obtain acceptable accuracy. These two requirements – precision and low computational cost, can be fulfilled using linear models defined using eigenvalue techniques. The Eigenvalue Method explicitly solves the groundwater flow problem by discretizing the space and providing a continuous-in-time solution formulated using a state equation. The hydraulic heads and the exchange of flow between the surface water body and the aquifer can be efficiently computed using this equation. The method is applicable to aquifers with linear behaviour (confined or unconfined aquifer with hydraulic head changes that are small in comparison with the saturated thickness) and linear boundary conditions. This paper describes a methodology to simulate groundwater flow with non-linear boundary conditions using a state equation defined from a linear Eigenvalue Model; and gives a detailed formulation for Finite Difference spatial discretization. Application of this methodology conserves the computational advantages of the Eigenvalue Method. It is based on correcting the non-linear boundary conditions by superposing fictitious stresses in the cells where these boundary conditions are modeled. The intensities of these additional stresses are obtained by solving a system of linear equations. These equations are defined by specifying that the volume exchange in each of these cells is equal to what would exist under non-linear boundary conditions. The methodology has been applied to simulate the groundwater flow of the “Molar” and “Vega Alta” aquifers in the Segura River Basin (south-eastern Spain), and the accuracy of the results have been demonstrated through comparison with those obtained using MODFLOW.