Polynomial approximation of equipotential lines for flow under a dam

In this study we explain a computational model that is developed based on polynomial solutions of the equations governing water flow beneath a dam. The results are extensions to the solutions typically obtained by finite difference (or finite element) methods that are in the form of discrete points on a predefined grid. Polynomial equations satisfying the governing equations and the boundary conditions are first derived for the equipotential functions. The coefficients of the polynomials are evaluated by the weighted least squares method. Then by using the well known relations between equipotential lines and stream lines, similar polynomial equations are obtained to describe flow lines. The method discussed in this paper allows for the complete discription of the flow domain by polynomial functions. The results show that polynomials are good representations of the equipotential and stream lines.