## 3 Comparison between Flow-3D, MIKE 3 FM, and 1D Exact Riemann Solver Predictions  
### Free Surface  
#### 3.1.1 Free Surface during the Early Stage  
Figures 6-8 show a comparison of free-surface profiles during the early stage along a wall of the testing flume [30] at different times using dry- and wet-bed conditions downstream. The figures also present free surface profiles with a 1D Ritter's analytical solution [5], which would serve as a means to check the accuracy and robustness of the simulated results in the numerical model. In all the free-surface profiles in Figures 6-9, the water depths (\(h\)) and horizontal distances (\(x\)) were transferred into dimensionless parameters with the initial water depth \(h_{0}\). An error analysis of the free-surface profile results obtained by the 1D analytical results and Flow-3D and MIKE 3 FM models are summarized in Table 1.  
Figure 5: Sensitivity analysis of the numerical simulation using MIKE 3 FM for the different mesh sizes of the experiments in Reference [30]. Figure 6: Comparison between observed and simulated free surface profiles at dimensionless times \(T=t(g/h_{0})^{1/2}\) and for dry-bed (\(\alpha=0\)). The experimental data are from Reference [30]. Figure 7: Comparison between observed and simulated free surface profiles at dimensionless times \(T=t(\xi/h_{0})^{1/2}\) and for a wet-bed (\(\alpha=0.1\)). The experimental data are from Reference [30]. Figure 8: Comparison between observed and simulated free surface profiles at dimensionless times \(T=t(\delta/h_{0})^{1/2}\) and for the wet-bed (\(\alpha=0.4\)). The experimental data are from Reference [30]. Good consistency was found between the RANS results obtained by Flow-3D and measurements for the dry-bed test (\(\alpha=0\)), as shown in Figure 6. The surface profiles were originally parabolic and \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Water Depth** & \multirow{2}{*}{**Time \(T\) (-)**} & \multicolumn{3}{c}{**RMSE**} \\ \cline{3-5}
**Ratios** & & **Analytical Solution** & **Flow 3D** & **MIKE 3 FM** \\ \hline \multirow{6}{*}{0} & 1.127 & 0.07 & 0.04 & 0.05 \\  & 2.755 & 0.05 & 0.06 & 0.06 \\  & 3.882 & 0.04 & 0.02 & 0.04 \\  & 5.009 & 0.03 & 0.02 & 0.04 \\  & 6.637 & 0.03 & 0.02 & 0.04 \\ \hline \multirow{6}{*}{0.1} & 1.565 & 0.10 & 0.09 & 0.09 \\  & 2.379 & 0.07 & 0.05 & 0.07 \\  & 4.007 & 0.10 & 0.08 & 0.09 \\  & 6.511 & 0.10 & 0.08 & 0.10 \\  & 8.891 & 0.05 & 0.04 & 0.05 \\ \hline \multirow{6}{*}{0.4} & 1.565 & 0.09 & 0.06 & 0.09 \\  & 2.379 & 0.08 & 0.02 & 0.07 \\ \cline{1-1}  & 4.007 & 0.07 & 0.05 & 0.06 \\ \cline{1-1}  & 6.511 & 0.05 & 0.03 & 0.04 \\ \cline{1-1}  & 8.891 & 0.04 & 0.04 & 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: RMSE values for the free surface profiles observed by [PERSON] and [PERSON] [30]. Figure 9: Experimental and numerical comparison of free surface profiles \(h/h_{0}(x/h_{0})\) during late stages at various dimensionless times \(T\) after the failure in the dry-bed by [PERSON] et al. [39]. the wavefront became convex as time progressed. However, the 3D SWE results obtained by MIKE 3 FM and the 1D analytical results of [PERSON]'s solution showed small deviations from the measurements, favoring the less obvious convex solution, especially at the early initial stage. The experimental profiles after the dimensionless time \(T=5.009\) were close to those computed by all three models, with \(T=t(g/h_{0})^{1/2}\). The simulated wavefront in the downstream region (\(x/h_{0}>0\)) using MIKE 3 FM moved more slowly than the measurements and the results of Flow-3D, indicating that the wavefront in the upstream reservoir (\(x/h_{0}<0\)) moved faster than the measurements and the other results. It was observed that the two numerical models and analytical solution generally had low values for the RMSE, with all of them below 0.08 at different times, which indicates that both types of solutions achieved acceptable results for the dry-bed case during the initial stage, while the Flow-3D model obtained the best RMSE result of 0.02 (Table 1).