## 3 Numerical Model
### Solution Domain, Boundary and Initial Conditions
However, the SWE disagreed with the other results for the time interval \(t=2\)-3 s. The levels of the peaks were determined better than W1 at the P5 generally, whereas undulations were not well represented in terms of time steps of the wave crests. Although the comparison results are in good agreement overall, it can be said that the celerity of the small waves was not computed precisely by both numerical methods at this point. The discrepancies between experimental and numerical models can be summed up in Table 2 in terms of the MAPE (Mean Absolute Percentage Error) of water level time histories in measuring points P1, P3, P4, and P5. The P2 error calculations in the table were not reported in the table, because, as explained before, the P2 sensor gave erroneous results between the 0-2 s time interval in all experiments, as it could not read water depths. In general, the error rates in the SWEs were higher than the RANS for all of the simulations. As mentioned above and observed in Figures 7, 9 and 11, the highest errors were observed during the passage of the reflected wave for all cases (e.g., 12.54% for the RANS and 15.37% for the SWEs in test D1). The smallest error rates were observed at P1 located in the reservoir for the SWEs and the RANS (e.g., 3.99% for the RANS and 4.01% for the SWEs in test D1). As expected, although the SWEs still appear as a well-established choice and most of the existing models developed to solve these equations can produce valuable results for flood prediction, they are not as efficient in simulating the observed dam-break wave propagation process in complex flows due to turbulence, air entrainment, hydraulic jumps, etc., which cannot be reproduced with hydrostatic pressure acceptance and shock wave representation. A 3D approach is to be preferred, at least with the RANS. The present work investigates the capability and the performance of the two models to simulate dam-break flows in an enclosed domain with both dry and wet cases. It can be observed that the solution obtained from the VOF-based RANS numerical model reproduces, \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **P1** & & **P3** & & **P4** & & **P5** \\ \hline  & **RANS** & **SWEs** & **RANS** & **SWEs** & **RANS** & **SWEs** & **RANS** & **SWEs** \\ \hline
**D1** & 5.17 & 2.91 & _9.45_ & 14.74 & _4.99_ & 12.57 & _12.54_ & 15.37 \\
**W1** & 3.99 & 4.01 & _8.08_ & 16.71 & _4.42_ & 9.03 & _10.79_ & 11.50 \\
**W2** & _3.90_ & 3.84 & _8.83_ & 13.01 & _3.63_ & 7.16 & _8.16_ & 10.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: MAPE (Mean Absolute Percentage Error) error analysis referred to the comparison between numerical (RANS and SWEs, respectively) and experimental results for water level time histories at measurement points P1, P3, P4, and P5. with reasonable accuracy, the propagation of the negative wave induced by the strong reflection of the dam-break flow against the side and end walls of the channel, though requiring a higher computational time. On the contrary, the SWEs simulations provided results which had little disagreement with the observed ones but with the advantage of less computational time, which would be even more significant in real-case and/or real-scale applications. As an example, considering the case W1, the run-time was approximately 2 min for the SWEs and 116 min for the RANS for a 10 s solution time, respectively, running the simulation a computer with an Intel Core i7 2.8 GHz 16 GB RAM. Hence, SWE-based numerical models are still preferable over RANS-based models for problems requiring large computational domains, especially where the vertical acceleration is insignificant due to fewer computational efforts and time. Usually, fine meshes are needed in numerical simulations in order to better represent irregular topographies and obtain more accurate results.