| Title |
An Application of the HLLL Approximate Riemann Solver to the Shallow Water Equations |
| Authors |
황승용(Hwang, Seung-Yong) ; 이삼희(Lee, Sam Hee) |
| DOI |
https://doi.org/10.12652/Ksce.2012.32.1B.021 |
| Keywords |
천수방정식;근사 Riemann 해법;HLL 기법;HLLL 기법 shallow water equations;approximate Riemann solver;HLL scheme;HLLL scheme |
| Abstract |
The HLLL scheme, proposed by T. Linde, determines all the wave speeds from the initial states because the middle wave is evaluated by the introduction of a generalized entropy function. The scheme is considered a genuine successor to the original HLL scheme because it is completely separated form the Roe's linearization scheme unlike the HLLE scheme and does not rely on the exact solution unlike the HLLC scheme. In this study, a numerical model was configured by the HLLL scheme with the total energy as a generalized entropy function to solve governing equations, which are the one-dimensional shallow water equations without source terms and with an additional conserved variable relating a concentration. Despite the limitations of the first order solutions, results to three cases with the exact solutions were generally accurate. The HLLL scheme appeared to be superior in comparison with the other HLL-type schemes. In particular, the scheme gave fairly accurate results in capturing the front of wetting and drying. However, it revealed shortcomings of more time-consuming calculations compared to the other schemes. |