An Enclosing Analytic Element

Abstract

The main contributions described in this thesis are two-fold: 1. A new analytic element for a closed boundary of a chosen shape that may contain internal elements. The element, referred to as the enclosing analytic element, is valid for steady three-dimensional flow. We outline the general method for constructing these new analytic elements and provide several examples: (1) an elliptic enclosing element, (2) a square enclosing element, (3) a rectangular enclosing element, and (4) a slotted enclosing element. We combine the enclosing analytic element with other established analytic elements via superposition, including uniform flow, recharge, wells, line-sinks, and elliptic lakes. 2. A new technique for expanding the original shape into a family of shapes. Each new shape within the family set results in a reduction in the sharpness of the corners. We refer to these new shapes as smooth boundary shapes.