A staggered method for the shallow water equations involving varying channel width and topography

We propose a staggered-grid finite volume method for solving the shallow water equations involving varying channel width and topography in one dimension. The method is an extension of an existing staggered conservative scheme for shallow water flows. One great advantage of the numerical method is that it does not need any Riemann solver in the flux calculation, so the numerical computation is cheap. We obtain that the method is able to solve a wide range of problems. The proposed method is well balanced and of the first order of accuracy.