An Improved Surface Gradient Method for the Computation of Hyperbolic-Type Shallow-Water Equations on Irregular Bathymetry

A simple but robust numerical scheme is proposed for the analysis of hyperbolic-type shallow-water equations with source terms adequate to describe subcritical and supercritical flows, and continuous and discontinuous flows. Although many numerical techniques such as approximate Riemann solvers are reported to analyze transcritical flows, the applications are still limited to only ideal problems due to a numerical unbalance between the flux and source terms. In this study, an improved surface gradient method is newly proposed to balance between flux and source terms. The MUSCL-Hancock scheme and HLLC approximate Riemann solver are employed in the new numerical model. Several examples including transcritical steady state flows, unsteady dam break flows on a wet and dry bed, and flows on a varying topography are tested. Very accurate and reasonable computed results are obtained.