PERFILES NO HIDROSTÁTICOS DE LÁMINA DE AGUA EN CANALES COMPUESTOS: UN MÉTODO NUMÉRICO IMPLÍCITO

Abstract

Free surface profiles in natural streams show singular features near in-stream structures or in the vicinity of critical depth passing points. The computations of those profiles allow to hydraulicians to assess flow discharge and flooding zones in compound channels, which highly affect to further technical decisions. Mainly due to the presence of non-hydrostatic pressure distribution, the free surface is no longer horizontal in the vicinity of free overfalls, which is wrongly predicted by means of the gradually-varied theory. The rapidly-varied theory is useful to accurately predict those undular profiles. In a previous work, the Boussinesq-type non-hydrostatic equations for compound channels along with a momentum approach showed greater results than an energy approach for undulated free surface computations near overfalls. The system of equations was solved using the 4th-order Runge-Kutta method. The free surface solution is reached by trying different free surface slopes at the upstream boundary. However, this method becomes costly in terms of computation efforts as the process is non-automatic. This study presents an implicit numerical method to solve the high-order Boussinesq-type non-hydrostatic equations for compound channels using momentum. A Jacobian matrix is determined to be introduced into a Newton-Raphson method. The solution is therefore presented as automatically convergent.