Open Water Flow in a Wet/Dry Multiply-Connected Channel Network: A Robust Numerical Modeling Algorithm

• Published in: Pure and applied geophysics Vol. 177; no. 7; pp. 3421 - 3458
• Main Authors: Kivva, Sergii, Zheleznyak, Mark, Pylypenko, Oleksandr, Yoschenko, Vasyl
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.07.2020; Springer Nature B.V
• Subjects: Algorithms; Computer simulation; Conservation; Conservation equations; Conservation of momentum; Continuity equation; Drying; Earth and Environmental Science; Earth Sciences; Exact solutions; Geophysics/Geodesy; Mathematical models; Momentum; Numerical analysis; Numerical experiments; Numerical simulations; Reconstruction; Robustness (mathematics); Shallow water; Supercritical flow; Water flow; wetting/drying; Saint–Venant equations; central-upwind scheme; Channel network with irregular geometry; well-balanced; positivity preserving
• ISSN: 0033-4553; 1420-9136; 0033-4533; 1420-9136
• DOI: 10.1007/s00024-020-02416-0

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 the momentum conservation equation provide positivity preserving and well-balanced features of the scheme for various wet/dry states. We use two models based on the 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 subcritical and supercritical flows 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 an initially dry channel network shows the merits of the new numerical algorithm to simulate the subcritical/supercritical open water flows in the networks.