Closed Analytic Elements with Flexible Geometry

Abstract

A simple and fast treatment of hydrogeologic features with irregularly shaped boundaries in two-dimensional analytic element groundwater flow models is presented. The star domain shapes of the features are restricted to closed shapes represented as smooth and continuous single-valued functions of distance from a focus point, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>r</mml:mi><mml:mo>ˆ</mml:mo></mml:mover><mml:mfenced><mml:mi>θ</mml:mi></mml:mfenced></mml:math> . The element can be used to treat a variety of boundary and continuity conditions, including those of irregularly shaped lakes or heterogeneities in hydraulic conductivity. The new element is demonstrated via some simple illustrative test cases and shown to be efficient, accurate, and much simpler to implement than existing solutions for irregular shapes.