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Journal of Korean Society of Coastal and Ocean Engineers > Volume 32(6); 2020 > Article
J Korean Soc Coast Ocean Eng 2020;32(6): 569-574. doi: https://doi.org/10.9765/KSCOE.2020.32.6.569
불연속 갤러킨 음해법의 천수방정식 적용
이해균1, 이남주2
1단국대학교 토목환경공학과 교수
2경성대학교 토목공학과 교수
Applications of Implicit Discontinuous Galerkin Method to Shallow Water Equations
Haegyun Lee1, Namjoo Lee2
1Professor, Department of Civil and Environmental Engineering, Dankook University, 152, Jukjeon-ro, Suji-gu, Yongin-si, Gyeonggi-do 16890, Korea
2Professor, Department of Civil Engineering, Kyungsung University
Corresponding author: Haegyun Lee ,Tel: +82-31-8005-3172, Email: haegyun@dankook.ac.kr
Received: November 20, 2020;  Revised: December 21, 2020.  Accepted: December 23, 2020.
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ABSTRACT
Though the discontinuous Galerkin (DG) method has been developed and applied to shallow water equations mainly in explicit schemes, they have been criticized for the limitation in treatment of bottom friction terms and severe CFL conditions. In this study, an implicit scheme is devised and applied to some representative benchmark problems. The linear triangular elements were employed and the Roe numerical fluxes were adopted for convective fluxes. To preserve TVD property, the slope limiter was employed. As the case studies, the model is applied to the flow around the cylinders and the dam-break flow. Then, the results are compared with the experimental and numerical data of previous studies and good agreements were observed.
Keywords: shallow water equations, discontinuous Galerkin, implicit scheme, Roe numerical flux, slope limiter
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