The momentum-conserving simulation for shallow water flows in channels with arbitrary cross-sections

Abstract

The momentum-conserving staggered grid (MCS) scheme to simulate shallow water flows in channels of varying width and topography is revisited in this article. Here, we modify the MCS scheme so that it can be applied to channels of arbitrary cross-section. The scheme is validated using steady analytical solutions for channels with rectangular and trapezoidal cross sections. We found that the method was capable of solving a wide variety of test cases; including subcritical, supercritical and transcritical steady flows and flows with hydraulic jumps. This MCS scheme could handle both steady and unsteady problems. In the implementation of a channel with arbitrary cross sections, the simulation depicts the time-lapse evolution of the water level toward the steady state. These results were consistent with previous findings in the literature. All numerical experiments carried out here demonstrate the merits of the numerical MCS scheme.