## 3 Numerical Model
### Solution Domain, Boundary and Initial Conditions
A complex 3D flow, with strong turbulences and significant air entrainment, is in fact observed as a result of the reflection from the side and end walls of the channel in the 3D experiment. Figures 4 and 5 show that the dam-break wave propagates faster in dry bed conditions (test D1) than in the wet bed cases (tests W1 and W2). In addition, in this latter case, the wavefront velocity decreased as the tailwater depth increased. This may be explained by the higher resistance, due to the higher water depth encountered by the propagating waves. Soon after the plate removal, the reservoir water rushing out from the channel bottom uplifted the tailwater. In contrast, after the wave reflection, the front velocity became higher for tests W2 than for tests W1 and D1. This can be imputable to the higher impact velocity of the positive wave to the end wall, to the higher potential energy stored in the final part of the flume, and to the higher time lag in forming negative wave for the dry-bed case, as compared to the wet-bed cases (see, for example, times \(t=0.6\)-\(1.2\) s). Moreover, a higher turbulence intensity with related significant energy dissipation was observed at the channel end for test D1 with respect to the wet-bed cases (see results for times \(t>0.8\) s in Figure 4). During the initial stages of the dam-break in the presence of tailwater, the pressure gradient forced the tailwater to move forward. Plunging-type wave breaking occurred, therefore, for the wet-bed tests, as shown in Figure 4 for \(t=0.4\) s and in Figure 5b. Accordingly, intensive turbulence appeared in the flow. As the tailwater depth increased (\(\alpha=0.4\)), spilling-type wave breaking occurred. It can also be noticed that the positive wave broke earlier as the tailwater decreased, as observed in Figures 4 and 5. Figures 4 and 5 show, again, that there is a significant difference in wavefront velocities between dry and wet-bed cases. Specifically, the wavefront velocity was higher for the dry-bed case, with an average value of about \(1.7\) m/s. In contrast, the average value was about \(0.9\) m/s for tests W1 and W2, and it decreased with an increasing depth ratio (\(\alpha\)). Figure 5: Dam-break wave propagation for all tests at \(t=0.4\approx\) (**a**) 2D experiments [22,52] and (**b**) 3D experiments. A very good agreement between experimental data and the numerical simulation results can be observed for all tests D1 and W1-W2. Therefore, FLOW-3D can predict the dam-break wave propagation with acceptable accuracy in an enclosed domain over both dry and wet beds. Numerical simulations have also been performed using SWEs. However, some differences can be noticed between the results obtained through the two different numerical schemes. As expected, the SWEs achieved a smaller accuracy than the RANS. The stage hydrographs of the numerical (RANS and SWEs) and experimental results (P1-P5 sensors) for test D1 are given in Figure 7.  
Figure 7: Comparison of experimental and numerical stage hydrographs (P1–P5 sensors) for test D1. Figure 8: Comparison between experimental (**a**) and numerical (**b**) results for test W1 (\(\alpha=0.1\)). After the sudden removal of the gate, the water in the upstream tank moved instantly to the downstream channel and the water level fell rapidly at P1 for both experimental and numerical results until approximately \(t\) = 5.5 s. After that, the water level increased slightly due to the reflected wavefront and remained constant with minor fluctuations. A small disagreement occurred at P1 for all phases between experimental and numerical results. It should be considered that P2 sensor graphs in all of the experiments gave erroneous results between the 0-2 s time interval, as the sensor could not read depths. This is because the waves reflected from the water surface could not reach the sensor. The response time of the sensor and curves of the flow surface were considered probable causes of the disagreement mentioned above.