Conformal mapping of groundwater flow fields with internal boundaries

An analytical approach is presented for solving problems of steady, two-dimensional groundwater flow with inhomogeneity boundaries. A common approach for such problems is to separate the problem domain into two homogeneous domains, search for solutions in each domain, and then attempt to match conditions, either exactly or approximately, along the inhomogeneity boundary. Here, we use classical solutions to problems with inhomogeneity boundaries with simple geometries, and map conformally the entire domain onto a new one. In this way, existing solutions are used to solve problems with more complex, and more practical, boundary geometries. The approach is general, but subject to some restrictions on the mapping functions that may be used. Using this approach, we develop explicit analytical solutions for two problems of practical interest. The first problem addresses aquifer interaction across a gap in an impermeable separating layer; flow regimes are defined and the interaction is quantified. The second solution represents flow in the vertical plane to a partially clogged stream bed that is partially penetrating the aquifer; the stream bed is modeled as a thin layer of low-permeability silt. Flow regimes for groundwater surface–water interaction are quantified analytically