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http://dx.doi.org/10.9765/KSCOE.2020.32.6.569

Applications of Implicit Discontinuous Galerkin Method to Shallow Water Equations  

Lee, Haegyun (Department of Civil and Environmental Engineering, Dankook University)
Lee, Namjoo (Department of Civil Engineering, Kyungsung University)
Publication Information
Journal of Korean Society of Coastal and Ocean Engineers / v.32, no.6, 2020 , pp. 569-574 More about this Journal
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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