A solution method for one-dimensional shallow water equations using flux limiter centered scheme for open Venturi channels

Abstract

The one-dimensional shallow water equations were modified for a Venturi contraction and expansion in a rectangular open channel to achieve more accurate results than with the conventional one-dimensional shallow water equations. The wall-reflection pressure–force coming from the contraction and the expansion walls was added as a new term into the conventional shallow water equations. In the contraction region, the wall-reflection pressure–force acts opposite to the flow direction; in the expansion region, it acts with the flow direction. The total variation diminishing scheme and the explicit Runge–Kutta fourth-order method were used for solving the modified shallow water equations. The wall-reflection pressure–force effect was counted in the pure advection term, and it was considered for the calculations in each discretized cell face. The conventional shallow water equations produced an artificial flux due to the bottom width variation in the contraction and expansion regions. The modified shallow water equations can be used for both prismatic and nonprismatic channels. When applied to a prismatic channel, the equations become the conventional shallow water equations. The other advantage of the modified shallow water equations is their simplicity. The simulated results were validated with experimental results and three-dimensional computational fluid dynamics result. The modified shallow water equations well matched the experimental results in both unsteady and steady state.