A discontinuous Galerkin method for two-dimensional shallow water flows
Article first published online: 14 NOV 2011
Copyright © 2011 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids
Volume 70, Issue 8, pages 939–960, 20 November 2012
How to Cite
Lai, W. and Khan, A.A. (2012), A discontinuous Galerkin method for two-dimensional shallow water flows. Int. J. Numer. Meth. Fluids, 70: 939–960. doi: 10.1002/fld.2721
- Issue published online: 5 OCT 2012
- Article first published online: 14 NOV 2011
- Manuscript Accepted: 9 OCT 2011
- Manuscript Revised: 26 AUG 2011
- Manuscript Received: 20 JUN 2011
- discontinuous Galerkin;
- finite element;
- incompressible flow
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.