Well-Balanced Variable Density Shallow Water Equations for Outfall Discharge Problems

Abstract

The importance of outfall and mixing problems calls for a simple, while accurate methodology for the simulation. Therefore, in this paper, a central upwind scheme for variable density shallow water system of equations is proposed over a triangular discretization of the domain. In this scheme, the well-balanced property is maintained so that the large oscillations and noises are avoided from the solution. The usability of this solution in the mixing and outfall problems is shown over a numerical example, also the accuracy and efficiency of the methodology is tested by comparing to another complex scheme in a practical largescale example. The comparison shows a significant advantage of the proposed methodology over other solutions, which is the very high efficiency while maintaining the accuracy of the results.