## 3 Numerical Model
### Solution Domain, Boundary and Initial Conditions  
The computational domain (1.00 m long, 0.50 m wide, and 0.20 m high) was subdivided into a structured mesh of fixed square cells in all of the simulations. Herein, as mentioned before, a minimum of two real cells had to be defined in each mesh block in the \(z\)-direction in order to apply VOF in the SWEs model. The size of the lower layer cell in the \(z\)-direction had to be large enough to contain all the water in that layer through the simulation. The software allowed dividing \(z\)-axis horizontally into two layers, with a lower layer of 0.17 m and an upper layer of 0.20 m. After a sensitivity analysis, a uniform mesh size of 0.005 m was used in three directions in the 3D RANS model and in two directions for the SWEs model for the whole computational domain. The mesh resulted in 200, 100, and 40 cells in the \(x\), \(y\), and \(z\) directions, respectively (Figure 3). The total number of cells was therefore 800,000 for the RANS and 40,000 for the SWEs. In the numerical computations, the sidewalls and the channel bottom were set as walls. At the top, over the air-water interface, the pressure boundary condition was assigned to account for the atmospheric pressure on the free surface. Since VOF defines the water surface, zero shear stress, and constant atmospheric pressure were applied [22]. A constant volume of fluid with dimensions of 0.25 \(\times\) 0.50 \(\times\) 0.15 m representing the reservoir was assigned as an initial condition (Figure 3). All channel walls were assumed to be smooth. The no-slip condition was defined as zero tangential and normal velocities. Once the initial and boundary conditions were established, the model was applied to the three different above-described tailwater conditions (D1, W1 and W2). Simulations were run for a duration of \(t=10\) s for each scenario. The time step \(\Delta t\) was determined according to the Courant-Friedrichs-Lewy (CFL) condition. When rapidly varied unsteady flows, including strong hydraulic jump and wave breaking were modelled with SWEs in FLOW-3D, a second-order monotonicity preserving momentum advection approximation was used in order to provide robust and accurate results. For the RANS simulations, first-order momentum advection approximation was used. An implicit scheme was used to solve the equations in both numerical models. The drag coefficient \(C_{D}\) was taken as 0.025, 0.030, and 0.04 at SWEs simulations for D1, W1, and W2, respectively. Different \(C_{D}\) coefficients were used to obtain better results. The \(C_{D}\) coefficient significantly affected the reflected wavefront and water depths. The default drag coefficient value of 0.0026, or the one calculated with roughness height \(k_{s}\) for glass using Equation (11), did not give very good results in determining the water depths and wavefront velocity after wave reflection. This topic is also a subject of future study on dam-break flows with strong reflections causing turbulence and significant air entrainment. Figure 3: 3D configuration of the numerical model for the RANS simulations (dry case). Additionally, the 3D test results were compared visually with the results of the 2D test performed by [PERSON] and [PERSON] [22] and [PERSON] and [PERSON] [52] in a channel with a rectangular cross section for the same depth ratios at the initial stages of the dam-break wave. In Figure 5, instead, the experimental results at time \(t=0.4\) s were plotted for all tests, comparing longitudinal and top views (2D and 3D experiments, respectively). In the 2D experiments, the current wave confined within a rectangular channel can be simulated as propagating in one direction. However, in the scenarios considered here, where the dam hole (and consequently the initial cross-section of the wave) was smaller than the channel cross-section, the flow cannot be treated as 1D flow strictly with a preferential propagation direction. Due to the circular propagation and wave breaking in all directions, a 3D simulation was therefore necessary.