Abstract

A finite volume second-order accurate Godunov-type solution of two-dimensional shallow water equations in boundary-fitted curvilinear coordinates has been presented in this paper. Flux difference splitting with Roe’s scheme is used for approximation of numerical flux. The simple and robust surface gradient method (SGM) of Zhou et al. is employed for treatment of source terms over irregular bed topographies to ensure C-property of the scheme. The scheme is simple, shock capturing and able to handle complex geometries with irregular bed topography. The results show very good agreement with analytical solutions.

Keywords: Godunov-type solution, Riemann solvers, C-property, shallow water equations