Numerical analysis of gradually varied flow in open channels using Runge-Kutta methods

In this thesis, the numerical solution of gradually varied flow (GVF) in open channels is investigated using high-order accurate explicit and implicit Runge-Kutta methods. The differential equation representing the water surface profile is solved using fourth-order Runge-Kutta (RK4) methods, and the computations are applied to two trapezoidal prismatic channel cases representing different hydraulic conditions. The obtained results are compared with reference solutions from the literature, showing that both methods offer high accuracy and numerical stability. Notably, the implicit RK4 method yielded lower total absolute error compared to the explicit method, demonstrating its superior stability characteristics. Consequently, Runge-Kutta-based numerical approaches are shown to be effective and reliable tools for modeling open channel flows in engineering applications.