Journal of Korean Society of Coastal and Ocean Engineers (한국해안·해양공학회논문집)

Korean Society of Coastal and Ocean Engineers (한국해안·해양공학회)
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Applications of Implicit Discontinuous Galerkin Method to Shallow Water Equations

불연속 갤러킨 음해법의 천수방정식 적용

  • Lee, Haegyun (Department of Civil and Environmental Engineering, Dankook University) ;
  • Lee, Namjoo (Department of Civil Engineering, Kyungsung University)
  • Received : 2020.11.20
  • Accepted : 2020.12.23
  • Published : 2020.12.31
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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.

천수방정식에 대한 불연속 갤러킨 기법 (DG)은 주로 양해법 기반으로 개발되어 적용되어 왔으나, 바닥마찰항의 처리, 과도한 CFL 조건 등의 불리한 점이 지적되어 왔다. 이에 대한 대안으로써, 본 연구에서는 음해법 기반의 모형을 개발하고 이를 적용하여 향후 가능성을 입증하였다. 본 논문에서 연구한 사례에서는 선형 삼각형 요소를 사용하였고, 수치흐름률로서 Roe 흐름률을 이용하였으며, TVD 특성 보존을 위한 기울기 제한자를 적용하였다. 적용 사례로서 실린더 주변의 흐름과 댐 붕괴류 문제 등에 대하여 적용하고, 기존의 실험치, 수치해와 비교하여 잘 일치함을 확인하였다.

Keywords

References

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