## 2 Materials and Methods
### Numerical Model and Simulation Setup  
#### 2.4.1 Flow-3D  
Flow-3D is a commercially available computational fluid dynamics (CFD) software package that is commonly used to model hydraulic structures, such as drainage culverts, spillways, and stilling basins. It calculates numerical solutions to RANS equations using a finite-difference approximation, and it also uses the volume of fluid (VOF) method for tracking the free surface. The solid geometry is represented using a cell porosity technique called the FAVOR method [40]. The governing continuity and RANS equations in Flow-3D for Newtonian, incompressible fluid flow are:  
\[\frac{\partial}{\partial x_{i}}(u_{i}A_{i})=0, \tag{8}\]  
\[\frac{\partial u_{i}}{\partial t}=\frac{1}{V_{F}}\left(u_{i}A_{j}\frac{ \partial u_{i}}{\partial x_{j}}\right)=-\frac{1}{\rho}\frac{\partial p}{ \partial x_{i}}+g_{i}+f_{i}, \tag{9}\]  
where \(u_{i}\), \(u_{j}\) = velocity component in the \(i\), \(j\) direction, \(A_{i}\), \(A_{j}\) = fractional area open to flow in the \(i\), \(j\) direction, \(t\) = time, \(V_{F}\) = volume fraction of fluid in each cell, \(\rho\) = fluid density, \(p\) = pressure, \(g_{i}\) = gravitational force in the \(i\) direction, and \(f_{i}\) = the diffusion transport term. In the present study, the equations for the motion are closed with the standard \(k\)-\(\epsilon\) model for turbulence closure, \(k\) is the turbulence kinetic energy, and \(\epsilon\) is the turbulent dissipation rate, and they were modelled in the dam-break problem application. The \(k\)-\(\epsilon\) model for turbulence closure is used to determine the turbulent viscosity to perform a simulation for the present two cases.  
Simulation Setup of Experiments by [PERSON] and [PERSON] [30]  
For the Flow-3D model, the RANS solution domain is 8.90 m in length, 0.30 m in width, and 0.30 m in height. The simulations are also conducted with coarser and finer meshes consisting of fixed  
Figure 3: Typical profiles of the dam-break flow regimes for [PERSON]’s analytical solution [9]: Wet-bed downstream.  
rectangular cells measuring 2 mm, 5 mm, 10 mm and 20 mm. The corresponding total cells of the mesh system are 667,500, 106,800, 26,700, and 6675. Figure 4 illustrates the differences between the simulated and measured free surface profile for different mesh sizes. Considering a wet bed case of \(\alpha=0.4\), an index of the root mean square error (RMSE) is calculated and presented. The computational time for the simulations at four mesh sizes is also shown in Figure 4. The simulated results are convergent under four grid sizes; only insignificant differences in the statistical variable RMSE are observed, but the computational efforts are quite different. Therefore, regarding both the accuracy and the computational cost, the grid spacing is set to \(\Delta x=\Delta z=0.005\) m. The upstream and lower boundaries are set as a wall, due to a lack of inflow. The downstream boundary is set as outflow for the dry-bed condition and as a wall for the wet-bed condition. The upper and channel sidewall boundaries are set as symmetrical.  
Simulation Setup of Experiments by [PERSON] et al. [39]  
For the Flow-3D model, the computational domain is discretized into rectangular cells that are 0.005 m long and 0.005 m high. The mesh system consists of 256,000 total cells. The settings of the boundaries are same as they are in Ozmen-Cagatay and Kocaman [30].