A Novel Method for Numerical Simulation of Gradually Varied Flow Profile Based on Adaptive Newton Raphson method

The basic equation of Gradually Varied Flow (GVF) describes the variation of water depth with flow process. Several methods have been developed for numerical solution of the water surface profile in GVF and one of the challenges of numerical integration is determining the appropriate integration spatial step size. In this paper a novel Adaptive Newton-Raphson method is developed for numerical solution of the GVF equation. In this method the spatial steps are determined by using error estimation during calculation, this procedure is smart and increases accuracy and speed of computation the water surface profile in GVF. Several examples were analyzed using the proposed method and compared with the results of previous researches and the accuracy of the proposed method was evaluated. The results indicate good accuracy of the proposed method in comparison with other methods. As shown in one of examples presented in the paper, the obtained results from 10 step of developed Adaptive Newton-Raphson methodapproximately equal with 90 step of standard direct step method.