Hydrodynamic Simulation of Open Channel Junctions Based on Momentum Conservation and Riemann Solution

The flow movement state at the junctions of open channels is very complex, and one-dimensional high-precision numerical simulation still faces significant challenges. This paper established a mathematical model of hydrodynamics at the junctions of open channels, which was completely decoupled from branch channels and junctions. In terms of the junction connection equation, a new junction momentum conservation equation was proposed, which did not require any empirical coefficients and increased the lateral pressure caused by the change in section width. The paper constructed a junction supplementary equation based on the Riemann solution. In terms of open channel hydrodynamics, the conserved Saint-Venant equation was used as the governing equation. Based on the Godunov format, the HLLC-approximate Riemann solver was used to calculate the interface flux. The results of the confluence case demonstrate that compared with measured values, the proposed method yields relatively small computational errors and shows significant superiority over the Taylor formula. In the diversion case, verification using two-dimensional hydrodynamic calculations reveals that the deviation in the branch channel diversion ratio between one-dimensional and two-dimensional unsteady flow simulations is merely 0.29%, while the relative error in the peak flow calculation remains below 1%. The research results provide a new method for the high-precision numerical simulation of hydrodynamics at the junction of one-dimensional open channels.