Source term treatment of SWEs using surface gradient upwind method

Abstract

Owing to unpredictable bed topography conditions in natural shallow flows, various numerical methods have been developed to improve the treatment of source terms in the shallow water equations. The surface gradient method is an attractive approach as it includes a numerically simple approach to model flows over topographically-varied channels. To further improve the performance of this method, this study deals with the numerical improvement of the shallow-flow source terms. The so-called surface gradient upwind method (SGUM) integrates the source term treatment in the inviscid discretization scheme. A finite volume model (FVM) with the monotonic upwind scheme for conservative laws is used. The Harten–Lax–van Leer-contact approximate Riemann solver is used to reconstruct the Riemann problem in the FVM. The proposed method is validated against published analytical, numerical, and experimental data, indicating that the SGUM is robust and treats the source terms in different flow conditions well.

Keywords:

• Finite volume model
• Harten–Lax–van Leer-contact solver
• monotonic upwind scheme
• source term
• surface gradient upwind method
• well-balanced scheme

Acknowledgements

Dr Jaan Hui Pu would like to thank Dr Khalid Hussain and Prof Simon Tait, University of Bradford, UK, for their guidance on SWE modelling during his PhD studies. Dr Songdong Shao acknowledges the support of the Royal Society International Travel Grants 2010/R4 Travel for Collaboration (TG102591).