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Two-Reservoir Problems: Revisited
Simulation of unsteady flow in open channels has always been of great interest to the hydraulic engineers. In the present study, the objective is to model and assess the shock phenomenon within a steep channel connecting two reservoirs. The dynamic nature of water level in the downstream reservoir creates a chain of events in the channel corridor which is the main focus of the current article. After a critical review of conventional textbooks on two-reservoir problems, the water level in the downstream reservoir is assumed to be changing as opposed to be stationary. Here, the main problem is to investigate the impact of state variables selection on possibility of capturing the dynamics of shock wave using conservation form of the Saint–Venant equations. The second component of flux vector is of momentum nature for a combination of Q and the pressure field variables (i.e., A, h, and Z) while it is of energy nature when u is combined with the pressure field variables. The governing equations in both groups are solved via finite volume and various flavors of finite difference codes written in MATLAB environment and the results are compared and contrasted with a program so-called FLDWAV. Numerical results confirm the fact that the state variables have to be chosen with great care in reference to the process under consideration. In conclusion, hydraulic engineers have to be warned upon wise implementation of numerical schemes when it comes to interaction among such terms as conservation, non-conservation form of Saint–Venant equations along with the state variables considered. The animation of chain of events emerged from computer programming can be used as an effective tool for educational purposes as the chain of events cannot be reproduced in the laboratory.
Journal Article