The Momentum Conserving Scheme for Two-Layer Shallow Flows

Abstract

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.

A novel technique for implementing the finite element method in a shallow water equation

“…In this section, our proposed scheme [ 10 ] will be used to simulate the water drop with an absorbing boundary [ 29 ] in four directions.…”

“…The shallow water wave equation (SWE) is a partial differential equation that enables us to gain a deeper understanding of physical phenomena in shallow environments. Assuming the horizontal length scale is greater than the depth scale, the SWE widely use to describe various real-world phenomena, for example: standing waves [ [1] , [2] , [3] , [4] ], wave refraction [ 5 ], dam break [ 6 ], internal wave generation in the strait [ [7] , [8] , [9] , [10] ], tsunami propagation in near-shore areas [ 11 ], and etc.…”