Author(s): Haegyun Lee; Nam-Joo Lee
Linked Author(s): haegyun Lee
Keywords: Discontinuous Galerkin; Runge-Kutta; Slope Limiter; Transcritical Flow; Shallow Water Equations
Abstract: Numerical solutions of 1D and 2D shallow water equations are presented with Runge-Kutta discontinuous Galerkin (RKDG) finite element method. For 1D problems, the transcritical flows such as dam-break flows and a flow over a hump with hydraulic jump were simulated and the numerical solutions were compared with the exact solutions. As a formulation of approximate Riemann solver, the local Lax-Wendroff (LLF) fluxes were employed and minmod slope limiter was used for 1D flows. For 2D applications, the classical problems of lateral transition were simulated. The HLL fluxes were adopted and a van Albada type gradient-reconstruction type slope limiter was applied. For the time integration, 3rd-order and 2nd-order TVD Runge-Kutta schemes were used for 1D and 2D simulations, respectively. In all case studies, good agreement was observed.
Year: 2013