Least-Squares Finite-Element Evaluation of Flow Nets

Abstract

A novel least-squares implementation of the finite-element method is presented to evaluate stream functions in the solution of field problems. The method is programmatically similar to the solution of the Laplace equation, and is based on the development of a stream field that is orthogonal to an already calculated potential field. The main advantage of the method comes from the fact that it eliminates the need of identification of boundary conditions for the stream functions. Implementation of this method requires that the Laplace equation be solved first to calculate the nodal potentials. The Laplace equation, with an identity conductivity matrix is then solved again to calculate the nodal values of the stream functions. One arbitrary boundary condition is sufficient for the second solution. Examples of cofferdam and curtained dam flow with isotropic as well as orthotropic soil conductivity are presented to demonstrate the method.