On the unidirectional free-surface flow behavior in trapezoidal cross-sectional open-channels

In this paper, consideration was given to the numerical prediction of free-surface wave behavior in trapezoidal open-channels. The Mac-Cormack scheme was implemented for the numerical discretization of the 1-D Extended St.-Venant equations, based on the Prandtl power law as a momentum correction coefficient. To verify the validity of the used numerical technique, the computed results were compared with experimental data and alternative numerical solutions quoted in the literature. These comparisons demonstrated that the results issued from the discretization of the 1-D Extended St.-Venant equations led to a more realistic description of the wave behavior than the ones obtained from the discretization of the 1-D Conventional St.-Venant equations. Furthermore, the results obtained by the developed numerical solver agreed well with those obtained by the Finite Element Method. However, the former solver was more advantageous than the latter with regard to computational time saving. The test cases addressed the trapezoidal particular shape of the open-channel cross-section. The findings highlighted that the adequate selection of the geometric characteristics of the open-channel cross-section could improve significantly the efficiency of these structures. Particularly, results demonstrated that the selection of an optimum side slope of the trapezoidal cross-section led to a maximum flow-rate while preserving a low value of the wetted cross-section area. •The extended 1-D St.-Venant Equations, based on the Prandtl power law was applied to predict the wave behavior in trapezoidal open-channel.•The results issued from the discretization of the Extended St.-Venant Equations lead to a realistic description of the wave behavior.•The induced waves have a dual relevance on the unreliability of open-channels, including important magnitudes of hydraulic drop and bore.•The optimum side slope of the trapezoidal section of canals allows a maximum flow-rate under a low value of the wetted cross-section area.