Solution Strategies in GFLOW

The groundwater flow problem in GFLOW is formulated in terms of the analytic element method (AEM), which is a variant of the Boundary Integral Equation Method (BIEM). Within the AEM a solution is sought for the a priory unknown “strength” parameters of the analytic elements. The strength parameter of a line-sink is its extraction rate σ [m/day], which is constant along the line-sink (Haitjema, 1995 section 5.1.2 and Strack and Haitjema, 1981a). The strength parameters for a line-doublet define the jump in the discharge potential s [m/day] generated across the line-doublet (Haitjema, 1995 section 5.1.3 and Strack and Haitjema, 1981b). The strength parameter for a head specified well is its pumping rate Q [m/day] (Haitjema, 1995 section 3.1.8), while the strength parameters for a partially penetrating well define the linear and singular sink densities along a three dimensional line-sink at the well axis (Haitjema, 1995 section 4.2.1). Most strength parameters are a priory unknown, but for each strength parameter a boundary condition can be formulated at a collocation point, usually selected at the line-sink or line-doublet itself. Each analytic element influences the discharge potential everywhere, linearly proportional to the value of its strength parameter or parameters. Consequently, the solution procedure for the unknown strength parameters xi gives rise to set of linear equations: aijxj = bi (1)