Numerical Modeling of Shock Wave Propagation and Flow In Open-Channel Networks

Dr. Mustafa M. Aral, Dr. Yi Zhang and Dr. S. Jin
Multimedia Environmental Simulations Laboratory
School of Civil and Environmental Engineering
Georgia Institute of Technology
Atlanta, Georgia 30332

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One of the most challenging problems in numerical simulation of flow in open-channel networks is the shock propagation problem, especially, for transcritical flow in which both supercritical and subcritical flows exist within the computational domain. A new-type shock-capturing relaxation-based scheme and a hybrid algorithm were proposed for simulation of flow and shock wave propagation in open-channel networks. The proposed relaxation-based scheme is based on the construction of relaxation system that approximates the original nonlinear system of conservation equations for a small relaxation time. Due to linear nature of the convection of the relaxation system, one does not need to use time consuming Riemann solver and the local characteristic decomposition. This leads to a simple and efficient scheme when compared with other modern shock capturing methods. Furthermore, by combining the relaxation-based scheme with the Method of Characteristics (MOC), a hybrid algorithm for flow simulation in open channel networks was proposed. This hybrid algorithm solves St. Venant equations together with junction equations, and can be applied to shock wave propagation in open-channel networks. Various numerical tests and examples were studied, and the results showed that the method can capture the shock accurately even for very strong shocks in open channel networks. Finally, a computer Modular Modeling System (RiverNET) with a user-friendly graphic interaction interface was developed for flow simulation in open-channel networks.

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