Application of Runge-Kutta Discontinuous Galerkin finite element method to shallow water flow

作者：Lee Haegyun^*

来源：KSCE Journal of Civil Engineering, 2014, 18(5): 1554-1562.

DOI：10.1007/s12205-014-0068-3

• discontinuous Galerkin
• Runge-Kutta
• slope limiter
• transcritical flow
• shallow water equations

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 bump 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 (Harten - Lax - van Leer) fluxes were adopted and a van Albada type gradient-reconstruction type slope limiter was applied. For the time integration, 3(rd)-order and 2(nd)-order TVD Runge-Kutta schemes were used for 1D and 2D simulations, respectively. In all case studies, good agreement was observed.

• 出版日期2014-6