Coupling of 1D and 2D models for river flow modelling
Résumé
1D river flow modelling approaches are generally inefficient when overbank flow occurs as the momentum transfers between the main channel and the overbank are neglected. 2D approaches require a precise meshing of the river bed to correctly take the topography into account, leading to high computational time. The existing implementations of the coupling 1D and 2D approaches take only mass transfer into account, while momentum transfers are neglected. A new 1D-2D methodology allows for a drastic reduction in the number of cells compared to a classical mesh by including each 1D cell within a single 2D cell that represents the floodplain. This also reduces the calculation time as the computation of the fluxes between 1D and 2D cells (that generally requires a small time step to ensure solution stability) is not necessary. The equations are solved using a finite volume approach that leads to a Riemann problem at the interface between two 1D (or 2D) cells that is solved using the HLLC solver. Instead of computing the flux between a 1D and a 2D cell, several hypotheses are used to determine the mass and momentum exchange. A numerical test case compares SW12D to a classical 2D approach on the basis of experimental values. A real world test case is also used to check the ability of SW12D to reproduce results produced by a classical 2D approach. In both cases, SW12D is more efficient and allows for a significant reduction of the computational duration.