An integral equation method to solve three dimensional confined flow to drainage systems

A new special type of the boundary element method (BEM) is presented to describe three-dimensional ground water movement for arbitrarily inclined drainage systems in a horizontal, confined, aquifer. The real drain pipe will be replaced by a system of polygonal line-sinks or sources. The discharge distribution over the length of the pipe can be approximated by a linear function, p on each element. As a particular application of superposition it is possible to use the method of images to realize the Neumann condition on the impervious boundaries. The infinite array of images of the drainage system can be replaced by a finite array of N images and two semi-infinite strips with the same specific discharge distribution. A collocation method leads to a linear equation system which determines the discharge approximation p and other interesting field values.