A conservative strategy to couple 1D and 2D models for shallow water flow simulation

Abstract

A 1D-2D coupled numerical model is presented in this work. 1D and 2D models are formulated using a conservative upwind cell-centered finite volume scheme. The discretization is based on cross sections for the 1D model rios. It is also applied to a real world configuration, where the flood wave propagation in the river bed is simulated by means of a 1D model and the inundation of the riverside is dealt with a 2D model. The computational gain is also analysed.

The FLO Diffusive 1D-2D Model for Simulation of River Flooding

“…On the other hand, water depths measured at Gauge 4 are different from the ones at Point 5 (in Figure 9a), where Point 4 is closest to the inlet of the floodplain and further away from the wall than Point 5. Observe the opposite in the results provided by Morales et al [10] and shown in Figure 10, where water depths at Points 4 and 5 are often undistinguishable at the adopted graphic scale, while smaller water depths are computed at Gauge 10 (see Figure 10a,b). For each simulation, the discharges leaving the domain and computed by the FLO model are very similar, and only the peak region is shown in Figure 11.…”

“…Due to the different resistance law in the 1D channel and in the floodplain, water depths computed over the coupled 1D-2D mesh are slightly higher than the ones over the 2D mesh, with the highest difference less than 0.01 m. On the opposite side, the results provided by Morales et al by their coupled procedure show large differences with respect to the ones computed by their 2D model. Morales et al [10] justify these differences with the choice of the Manning coefficient in the 1D channel and its adjustment due to coupling strategies. See the results of the two models, for both mixed and 2D meshes, shown in Table 1.…”

“…On the opposite, we do not modify the roughness coefficient values with respect to their original values. Moreover, we do not have to solve additional equations at the boundaries between the 1D and the 2D domain, unlike Morales et al [10]. In Scenario 3, initial conditions are the same used for Scenario 1, and the Neumann boundary condition has been replaced with a constant net rainfall, equal to 200 mm/h, applied above all of the floodplain, which provides a stationary entering discharge equal to 42.3 m 3 /s.…”

“…For each simulation, the discharges leaving the domain and computed by the FLO model are very similar, and only the peak region is shown in Figure 11. Morales et al [10] reduced the scatters between their 1D-2D and 2D models' results by modifying the Manning friction coefficient in the floodplain (see Figures 19 and 20 of their paper). On the opposite, we do not modify the roughness coefficient values with respect to their original values.…”

“…In standard explicit numerical 1D-2D coupling approaches (see, for example, [10]), the minimum between time step size required in the 1D and 2D domain is computed first, before solving separately of the 1D and 2D domains. The MAST scheme has shown stability with regard to the time step size, also for a Courant number (CFL) much greater than one [21].…”