Gradually varied flow profile based on adaptive pattern

Abstract

The basic equation of gradually varied flow (GVF) describes gradual changes in its water surface elevation. One of the challenges of numerical integration is determining the appropriate integration spatial step size. In this study, the water surface elevations in GVF are calculated by adaptive Runge–Kutta method and adaptive Newton–Raphson method. The steps are calculated using error estimation during calculation, this procedure is smart and increases accuracy and speed of computation of the water surface profiles in GVF. In order to show the efficiency and accuracy of these methods, the results of these two methods are compared with each other and the results obtained through direct Step method in several applications. The differences between the results are negligibly small. Finally, as practical applications the proposed methods are applied to study changes of water surface profile due to channel bed aggradation in GVF and cyclic looped network. Obtained results show 56% reduction in the CPU time compared with previous method (Simultaneous solution method).

Keywords:

• Adaptive pattern
• gradually varied flow
• Newton–Raphson method
• spatial step size
• the fifth-order adaptive Runge–Kutta method
• water surface profile