A central-upwind scheme for open water flow in a wet/dry multiply-connected channel network

TL;DR

This paper introduces a robust central-upwind numerical scheme for simulating complex open water flows in multiply-connected channel networks with arbitrary geometry and wet/dry conditions, ensuring accuracy and stability.

Contribution

It presents a novel reconstruction method for open water surfaces and exact source term integration, enabling well-balanced, positivity-preserving simulations of wet-dry transitions in complex networks.

Findings

The scheme accurately simulates subcritical and supercritical flows.

Numerical results agree well with exact solutions and experimental data.

The method effectively handles inundation and drying in channel networks.

Abstract

Our goal was to develop a robust algorithm for numerical simulation of one-dimensional shallow-water flow in a complex multiply-connected channel network with arbitrary geometry and variable topography. We apply a central-upwind scheme with a novel reconstruction of the open water surface in partially flooded cells that does not require additional correction. The proposed reconstruction and an exact integration of source terms for momentum conservation equation provide positivity preserving and well-balanced features of the scheme for various wet-dry states. We use two models based on continuity equation and mass and momentum conservation equations integrated for a control volume around the channel junction to its treatment. These junction models permit to simulate a subcritical and supercritical flow in a channel network. Numerous numerical experiments demonstrate the robustness of the proposed numerical algorithm and a good agreement of numerical results with exact solutions, experimental data, and results of the previous numerical studies. The proposed new specialized test on inundation and drying of initially dry channel network shows the merits of the new numerical algorithm to simulate the subcritical/supercritical open water flows in the network.