Developing Semi-Implicit and Reverse Explicit Numerical Models for simulation of hyperbolic Saint-Venant equations

New developed numerical models for solving hyperbolic Saint-Venant equations while having scientific and research value, play a significant role in the structural and performance management of hydraulic structures. In this paper, while developing two reverse explicit and semi-implicit numerical models based on Preissmann four points scheme, their application has been evaluated in a reach of Doab Samsami River, sub basin of Karoon. The reverse explicit has been developed based on Preissmann scheme and semi-implicit model has been developed using Preissmann scheme for distance derivatives with the Upwind scheme. Simulating of an output hydrograph using Manning roughness coefficient as setting parameter was performed with five accuracy criteria Nash-Sutcliff (NS), R-square (R2), Root mean square error and its standardized value (RMSE, NRMSE) and Developed discrepancy ratio (QDDR) for two calibration and verification periods. The amount of mentioned criteria for explicit and implicit models were calculated as (0.9352,0.9886,2.604,24.6,3.146) and (0.9843,0.9943,1.283,12.1,3.909) illustrating the reliable performance of the two models with the tangible superiority of the semi-implicit model. For more assurance of models performance, another hydrograph was simulated so that the values of NS, NRMSE and QDDR for semi-implicit and reverse explicit models were calculated (0.97,8.172,3.713) and (0.9339,12.28,2.612), respectively. These values proved the reliability and performance of the two models. The semi-implicit model had more accuracy than the explicit one in all cases. Solution stability in addition to high calculation efficiency is advantages of the semi-implicit model while leading to coupled complicated non-linear equations is its restriction.