A discontinuous Galerkin method for two‐dimensional shallow water flows

Abstract

SUMMARY A numerical scheme is developed for two‐dimensional, depth‐averaged, shallow water flows based on the DG method. In the shallow water equations, the pressure force term and the bed slope term are combined to eliminate numerical imbalance. The HLLC approximate Riemann solver is employed to calculate the numerical flux for the DG scheme. A slope limiting procedure used for compressible flows is adapted for modeling incompressible two‐dimensional flows. A simple treatment for modeling flow over initially dry bed is presented. To validate the scheme, numerical tests are conducted to simulate hydraulic jump, partial dam break, circular dam break, wetting and drying in parabolic bowl, and a real world dam break in the Toce River. Numerical results show that this scheme can accurately model shock waves, wetting and drying, and flows in the channel with varying geometry and bed topography found in natural channels. Copyright © 2011 John Wiley & Sons, Ltd.