Modeling the Flow Around Islands in Rivers Using a One-Dimensional Approach

Abstract

One-dimensional models are widely used for the simulation of flows in rivers. Around islands, the flow is divided and the discharge is distributed in the different branches. Such flow in a bifurcation is a typical two-dimensional feature, and representing the accurate partition of discharge might be a challenge in one-dimensional models depending on the flow conditions. In the present paper, a one-dimensional model is presented where the connections between the main river and the sub-channels are modeled as inner boundary conditions. These conditions are defined considering characteristic paths and conservation of the water head. Four flow configurations are considered: (i) a subcritical junction, (ii) a subcritical bifurcation, (iii) a supercritical junction, and (iv) a supercritical bifurcation. For the supercritical bifurcation, an additional condition is required and it is proposed here to partition the discharge in proportion to an equivalent cross-sectional width. The new one-dimensional model has been validated by comparing the results with those from a two-dimensional model for the four configurations. The comparison showed that the one-dimensional model predicts correctly the discharge and the water depth in each branch. Finally, the one-dimensional model was used to simulate the flow in a reach of the Meuse River (Belgium), showing good agreement with field data.