Abstract
One-dimensional (1D) Saint-Venant equations, which originated from the Navier–Stokes equations, are usually applied to express the transient stream flow. The governing equation is based on the mass continuity and momentum equivalence. Its momentum equation, partially comprising the inertia, pressure, gravity, and friction-induced momentum loss terms, can be expressed as kinematic wave (KIW), diffusion wave (DIW), and fully dynamic wave (DYW) flow. In this study, the method of characteristics (MOCs) is used for solving the diagonalized Saint-Venant equations. A computer model, CAMP1DF, including KIW, DIW, and DYW approximations, is developed. Benchmark problems from MacDonald et al. (1997) are examined to study the accuracy of the CAMP1DF model. The simulations revealed that CAMP1DF can simulate almost identical results that are valid for various fluvial conditions. The proposed scheme that not only allows a large time step size but also solves half of the simultaneous algebraic equations. Simulations of accuracy and efficiency are both improved. Based on the physical relevance, the simulations clearly showed that the DYW approximation has the best performance, whereas the KIW approximation results in the largest errors. Moreover, the field non-prismatic case of the Zhuoshui River in central Taiwan is studied. The simulations indicate that the DYW approach does not ensure achievement of a better simulation result than the other two approximations. The investigated cross-sectional geometries play an important role in stream routing. Because of the consideration of the acceleration terms, the simulated hydrograph of a DYW reveals more physical characteristics, particularly regarding the raising and recession of limbs. Note that the KIW does not require assignment of a downstream boundary condition, making it more convenient for field application.
Highlights
The one-dimensional (1D) Saint-Venant equations founded by Adhémar Jean Claude Barré deSaint-Venant are usually applied to express gradually varying open channel flows [1]
To neglect the different components in the momentum equation, the solutions can be cast as quasi-steady dynamic wave, gravity wave, noninertia wave, and kinematic wave flows [3]
Both the hydrograph and the error calculations clearly indicate that the dynamic wave (DYW) simulation achieves the most accurate results, whereas the kinematic wave (KIW) flow has the largest discrepancies
Summary
The one-dimensional (1D) Saint-Venant equations founded by Adhémar Jean Claude Barré de. This study uses the method of characteristics (MOCs) to solve the KIW, DIW, and DYW flows. Other research topics include channel constriction and obstruction issues [15], the effect of gravity for waves reduced by sudden flow stoppage [16], and the movement of particles along potential flow streamlines through junctions [17]. These can be studied using 1D Saint-Venant equations. Developed an one dimensional open-channel flow model, CAMP1DF, which includes the KIW, DIW, and DYW approximations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.