Study of Water Flow in Dams using Successive Over-relaxation

Free surface problems represent boundary value problems in which a portion of the boundary, the free surface, is unknown and must be determined as part of the solution. Classical rigorous and approximate procedures used to draw this line are limited to homogeneous and isotropic media with specific geometries. Currently, this can be determined using numerical methods such as the finite element method (FEM). Nevertheless, FEM requires the storing and handling of a large number of matrices to solve linear equation systems, increasing calculation time. The present article proposes an alternative to analyze free surface problems based on the numerical solution of finite difference equations using the successive over-relaxation method (SOR). Two techniques are implemented with the SOR method- Baiocchi's Solution and the Extended Pressure Method with the iterative Gauss-Seidel process. First, the theoretical basis for these methods are provided. Then, their applicability is described according to an analysis of unconfined flow in a homogeneous and a heterogeneous dam. As part of the results, the upper flow lines obtained with each technique and the flow networks calculated with the SOR method are presented and the use of finite difference equations to determine the hydraulic gradient and flow rate through the flow domain is described. Lastly, conclusions and recommendations for applying and optimizing the use of these techniques are provided.