An implicit 1D-2D deeply coupled hydrodynamic model for shallow water flows

The 1D-2D coupled hydrodynamic models have been widely developed, to simulate free-surface flows in large shallow water systems. A deeply coupled solution of 1D and 2D submodels refers to the involvement of a solution of flow equations across the 1D-2D interfaces, which will ensure the ability, stability and accuracy of the 1D-2D coupled model in simulating various flow regimes and scenarios. A deeply coupled solution is relatively easy for explicit submodels, but difficult for implicit submodels because of their complex iterative solutions. Techniques for coupling the solution of implicit 1D and 2D submodels are systematically studied, which includes a dimension reduction pretreatment for linking 1D and 2D grids, an upwind scaling method for solving the flow advection across a 1D-2D interface, a method for the drying-wetting simulation across 1D-2D interfaces, etc. The domaindecomposition prediction-correction method is extended to solve velocity-pressure coupling problems of the mixed 1D and 2D subdomains synchronously. Based on these techniques, a 1D-2D deeply coupled model is developed, which allows large time steps, requires only minor data exchange at 1D-2D interfaces, and can be well parallelized. Model test is first done using a real dam-break flow and a hypothetical periodic flow in an experimental flume, to demonstrate the ability of the new model in simulating unsteady supercritical and subcritical flows. The simulation results are shown to agree with the experimental measurements, the simulation results of an existing 1D-2D coupled model and the HEC-RAS. The second test uses a real large river-lake system, and the efficiency of the proposed model is compared with those of a pure 1D model, a pure 2D model and a newly reported 1D-2D coupled model (the proposed model is shown to run about 2 orders of magnitude faster than the newly reported model). Moreover, four 1D-2D coupled models, characterized by different levels of coupling degrees, are tested and compared. With the key physical terms of the governing equations being solved across the 1D-2D interfaces, the proposed model achieves essential improvements in accuracy compared to the loosely coupled model.