Approximate application of the method of images in fields with two boundaries intersected at angles between 180° and 90°

Abstract

In this paper, we introduce approximate analytical solutions for groundwater flows in semi-infinite fields confined by two rectilinear boundaries (both constant head or both impermeable), which are intersected at an angle between 90° and 180°. The solutions are based on the method of images. Their main special feature is that both boundary conditions are observed, at the expense of the continuity of the velocity field along a particular straight line. First, we discuss the range of application of each solution and the validity of the results, using physical arguments. Then we compare our results with numerical ones, obtained by Modflow, namely an established numerical tool. Discrepancies are generally small. The main attractive feature of the proposed approximate analytical procedures compared to numerical ones is that the computational load is much smaller at all stages: a) Introduction of fictitious boundaries to contain the flow field is reduced to definition of the radius of influence of the wells, b) No grid construction is required and c) Calculation of the hydraulic head is conducted separately at any point of the flow field. Moreover, accuracy of the results is good, compared to that of numerical methods, which depends on the dimensions of the respective grid.