Numerical modeling of open-channel flows with fixed and movable beds

This work presents numerical models for the analysis of steady and unsteady flow in open channels with fixed and movable beds. The fixed bed model numerically solves the two-dimensional unsteady flow equations by the explicit MacCormack scheme. The unsteady model is used to simulate steady flow by letting the solution converge to a steady state. The model uses governing equations in a channel-fitted coordinate system, convenient for computing flows in curved and meandering channels. A simple algebraic transformation of physical domain into a rectangular computational domain is discussed for application of the model to converging and diverging channels. Applicability of the model to simulate steady and unsteady, subcritical and supercritical flows is demonstrated. The movable bed models solve the flow equations along with the sediment continuity equation to predict bed level changes. The one-dimensional coupled movable bed model presented in this study solves all the governing equations simultaneously. This model is applied to compute bed level changes in straight alluvial channels due to aggradation and degradation. The two-dimensional, quasi-steady model assumes steady flow conditions during the bed level computations and the water-flow and sediment-transport equations are not coupled. Applicability of this model to predict long term bed evolution in curved alluvial channels is demonstrated. Comparison of numerical and experimental results shows that the models presented in this study satisfactorily simulate the basic features of many practical problems.