Abstract: This paper first summarizes four physically-posed requirements on the difference scheme used, i. e., conservation, upwindnss, positivity (or monotonicity-preserving), and high-resolution in discontinuities. In the recent over one decade, a lot of schemes satisfying these requirements have been proposed and widely used in gas dynamics. Among them, three types of schemes, including the flux-vector splitting (FVS), flux-difference splitting (FDS), and flux-corrected transport (FCT), are transferred to the computations for one-dimensional unsteady open channel flows, and related formulas are derived based on the concrete form of the Saint-Venant system of equations in consideration of the geometric irregulKrity of natural rivers. Finally, these methods are verified through a dam-break case study, yelding results that are close to each other, so that brilliant prospects of their applications can be foreseen.