The research on calculation of water surface profile in channel by Runge - Kutta method

The basic equation of steady gradually varied flow describes the variation of water depth with flow process. Because it´s difficult to be solved directly, the standard step method becomes the general way to calculate the water surface profile, which will entail many problems when the iteration method must be used. Thus the paper does a research on Runge-Kutta method to solve the differential equation directly avoiding these problems. Two calculation models for water surface profile are derived, both for prismatic channel, and also for non-prismatic channel. They can calculate the water surface profile from upstream or downstream. The function ode45 in MATLAB, taking Runge - Kutta method as the algorithm kernel, is selected to implement the calculation of two models. Finally two examples prove the correctness of the models, and high -precision feature of ode45 compared with the standard step method. The new way of calculating water surface profile is a reliable, simple and flexible method, easy to be popularized in engineering.