Computation of Gradually Varied Flow by Fourth Order Runge-Kutta Method (SRK)

The main hydraulic engineering activities related to flow in open channels involve the calculation of gradually varied flow profiles (GVF) (Subramanya, 1990); the same one that requires a considerable effort in the analysis and solution of the problems under consideration, such as: flooding of land due to the construction of dams, determination of flow profiles due to the various hydraulic structures in the channel and estimation of flood areas. This paper outlines an efficient algorithm of numerical solution of the differential Gradually Varied Flow (GVF) based on the Standard Fourth Order Runge-Kutta Method (SRK) for permanent flow in prismatic channels without resorting to tables or traditional interpolation techniques. The results show that the calculation procedure, implemented in MatLab, meets a high level of convergence and a very high computational efficiency in terms of accuracy and speed.

Keywords: Gradually varied flow, flow profiles, numerical solution