We consider the extension of the momentum conservative staggered-grid (MCS) scheme for flow simulation in channels with varying depth and width. The scheme is formulated using the conservative properties of the Saint-Venant equations. The proposed scheme was successful in handling various steady flows and achieved results that are in complete accordance with the analytical steady solutions. Different choices of boundary conditions have created steady solutions according to the mass and energy conservations. This assessment has served as a validation of the proposed numerical scheme. Further, in a channel with a contraction and a nonuniform bed, we simulate two cases of dam break. The simulation results show a good agreement with existing experimental data. Moreover, our scheme, that uses a quasi-1-dimensional approach, has shown some fair agreement with existing 2-dimensional numerical results. This evaluation demonstrates the merits of the MCS scheme for various flow simulations in channels of varying width and bathymetry, suitable for river flow modeling.

This paper confronts the numerical simulation of steady flows of fluid layers through channels of varying bed and width. The fluid consists of two immiscible fluid layers with constant density, and it is assumed to be of a one-dimensional shallow flow. The governing equation is a coupled system of two-layer shallow water models. In this paper, we apply a direct extension of the momentum conserving scheme previously used for solving the one layer shallow water equations. Computations of various steady-state solutions are used to demonstrate the performance of the proposed numerical scheme. Under the influence of a given flow rate, the numerical steady interface is generated in a channel topography with a hump. The results obtained confirm the analytic steady interface of the two-layer rigid-lid model. Furthermore, the same scheme was used with an additional artificial damping to simulate the maximal exchange flow in channels of varying width. The numerical steady interface agreed well with the analytical steady solutions.

We study a simple numerical scheme based on a new type of Finite Element Method (FEM) to solve the 1D Shallow Water Equations. In the new scheme, the surface elevation variable is approximated by a linear continuous basis function (P 1) and the velocity potential variable is approximated by the one-dimensional discontinuous linear non-conforming basis function ( P 1 N C ). Here, we implement the P 1 − P 1 N C finite element pair to solve the 1D Shallow Water Equations on a structured grid, whereas the Runge Kutta method is adopted for time integration. We verified the resulting scheme by conducting several simulations such as a standing wave simulation, and propagation of an initial hump over sloping bathymetry. The resulting scheme free from numerical damping error, conservative and both standing wave and shoaling phenomena are well simulated.

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Rapid flow downstream due to dambreak has a detrimental effect on the surrounding environment or, more dangerously, can be life-threatening. From a practical point of view, these flows are important to studies due to the limited dambreak real case data. This paper discusses the numerical modelling of the dambreak flow through a channel with three different contractions. Our goal here is to investigate the performance of a numerical model for solving the Saint-Venant equations using a momentum conserving staggered grid scheme (MCS). The scheme is the conservative formulation of the governing equations. Flows across channels of various widths and depths have been successfully simulated using a version of this scheme. In this work, we extend our previous work by simulating dambreak flow in a wave tank through several forms of contraction; trapezoidal and triangular. Our simulation results show good agreement with the experimental data in the literature. This assessment shows the merit of the scheme, which is suitable for dambreak flows in channels of varying width.