Well-Balanced Scheme between Flux and Source Terms for Computation of Shallow-Water Equations over Irregular Bathymetry |
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Authors: | Dae-Hong Kim Yong-Sik Cho Hyung-Jun Kim |
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Affiliation: | 1Graduate Student, Dept. of Civil Engineering, Texas A and M Univ., College Station, TX 77840. E-mail: soozawon@tamu.edu 2Professor, Dept. of Civil Engineering, Hanyang Univ., 17 Haengdang-dong, Seongdong-gu, Seoul 133-791, Korea (corresponding author). E-mail: ysc59@hanyang.ac.kr 3Graduate Student, Dept. of Civil Engineering, Hanyang Univ., 17 Haengdang-dong, Seongdong-gu, Seoul 133-791, Korea. E-mail: john0705@hanyang.ac.kr
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Abstract: | Although many numerical techniques such as approximate Riemann solvers can be used to analyze subcritical and supercritical flows modeled by hyperbolic-type shallow-water equations, there are some difficulties in practical applications due to the numerical unbalance between source and flux terms. In this study, a revised surface gradient method is proposed that balances source and flux terms. The new numerical model employs the MUSCL–Hancock scheme and the HLLC approximate Riemann solver. Several verifications are conducted, including analyses of transcritical steady-state flows, unsteady dam break flows on a wet and dry bed, and flows over an irregular bathymetry. The model consistently returns accurate and reasonable results comparable to those obtained through analytical methods and laboratory experiments. The revised surface gradient method may be a simple but robust numerical scheme appropriate for solving hyperbolic-type shallow-water equations over an irregular bathymetry. |
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Keywords: | Shallow waters Computation Bathymetry Numerical models Subcritical flow Supercritical flow |
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