## 3 Numerical Model
### Solution Domain, Boundary and Initial Conditions
The hydraulic jump was later than in reality, which means that the SWE underestimated the jump's velocity at P2 (\(t=2\)-\(4\) s). The agreement of the results increased with the decreasing oscillation for the rest of the plot. The behavior at the initial phase of the P3 sensor was similar to the P2 one, and the measured results were more successful. The hydraulic jump occurred just as for the previous probe. However, an almost 25% difference was calculated between the hydraulic jump heights of the two numerical results (\(t=2\) s). More undulations were observed compared to the P2 sensor, and the SWE results appeared inconsistent with the RANS and the experimental results (especially on the determination of the wave crests). Although there were some differences in the wave height and wave creity at the P4 sensor, the measured and computed results were generally in better agreement compared to the other downstream probes in the W1 case. In contrast, the results were quite in disagreement at the P5 sensor for the time interval \(t=0\)-\(2\) s. Three different peak levels were observed at that time interval, and the discrepancy between the results was dramatic. Also, for the same time interval, the RANS and SWE water depths were lower and higher than the experimental results, respectively, showing the great difference between their theoretical approaches for complex flow conditions due to the collision of the moving and reflected wave at the end of the tank. In this region, the height of the hydraulic jump was not well determined by both the numerical methods, and the oscillations were not represented by the RANS as good as they were for previous probes (\(t=\)\(2\)-\(10\) s). Figure 10 shows the comparison between the experimental data (on the left-hand side) and the numerical results calculated by the RANS (second and third columns) of the dam-break process evolution for test W2. From the visual comparison, it is can be clearly stated that there is a good agreement between the experimental and numerical results. The stage hydrographs for the test case W2 are shown in Figure 5:0 It is noticeable that the wave crests are sharper than for the W1 test, and the strong wave breaking cannot be seen here since the tailwater is higher in W2 test. It can be said that an increasing tailwaterlevel, with constant initial reservoir water depth, caused sharper wave crests and less wave break. Similar behavior was observed in an earlier study [22]. The agreement of the SWE results with the measured results was better than the RANS at P1 before \(t=4\) s. With the increasing undulations the SWE results disagreed with both the RANS and the experimental results. Although the sharp crests were occasionally predicted nearly as measured, the SWE generally produced straight lines for the undulations in all cases of the present study due to neglecting the vertical velocity components and assuming hydrostatic pressure distribution in this model. Similar behaviors with the previous test case were observed at the P2 sensor, especially on the failed measurement results for \(t=0\)-2 s. While the RANS and experimental results were in good agreement after the \(t=2\) s (except for the prediction of the wave crest at \(t=4\) s) the SWE determined the average water level almost properly. The numerical results disagreed with the experimental results at the initial phase of the P3 plot, predicting the wave crest height 30% more than in reality for different time steps (\(t=0\)-2 s). After that, the SWE results were below the other results until approximately \(t=5\) s. Then agreement increased, and less undulations were observed compared to the P3 sensor of the W1 test case. Even though many undulations occurred, P4 had the best agreement between the results, owing to the lower wave heights for the W2 among the downstream probes.