## 2 Materials and Methods
### Numerical Model and Simulation Setup
#### 2.4.2 MIKE 3 FM  
The MIKE 3 flow model FM is a modelling system based on a flexible mesh (FM) approach developed at the Danish Hydraulic Institute (DHI), and it is based on a finite volume, unstructured mesh approach. The flexible mesh is most suitable for irregular water body boundaries. The MIKE 3 FM is based on the numerical solution of the 3D incompressible RANS equations when subject to the Boussinesq approximation and an assumption of hydrostatic pressure. The continuity equation and horizontal momentum equations [41] can be written as  
\[\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w }{\partial z}=S, \tag{10}\]  
Figure 4: Sensitivity analysis of the numerical simulation using Flow-3D for the different mesh sizes of the experiments in Reference [30]. \[\frac{\partial u}{\partial t}+\frac{\partial u^{2}}{\partial x}+\frac{ \partial vu}{\partial y} +\frac{\partial wu}{\partial z}\] \[=fv-\delta\frac{\partial\eta}{\partial x}-\frac{1}{\rho_{0}} \frac{\partial p_{a}}{\partial x}-\frac{\mathcal{S}}{\rho_{0}}\int_{z}^{\eta} \frac{\partial\rho}{\partial x}dz-\frac{1}{\rho_{0}h}\left(\frac{\partial s_{ xx}}{\partial x}+\frac{\partial s_{xy}}{\partial y}\right)+F_{u} \tag{11}\] \[+\frac{\partial}{\partial z}\left(v_{t}\frac{\partial u}{\partial z }\right)+u_{s}S,\] \[\frac{\partial v}{\partial t}+\frac{\partial v^{2}}{\partial y}+ \frac{\partial uv}{\partial x} +\frac{\partial wv}{\partial z}\] \[=-fu-g\frac{\partial\eta}{\partial y}-\frac{1}{\rho_{0}}\frac{ \partial p_{a}}{\partial y}-\frac{\mathcal{S}}{\rho_{0}}\int_{z}^{\eta}\frac {\partial\rho}{\partial y}dz-\frac{1}{\rho_{0}h}\left(\frac{\partial s_{yx}}{ \partial x}+\frac{\partial s_{yy}}{\partial y}\right)+F_{v}\] (12) \[+\frac{\partial}{\partial z}\left(v_{t}\frac{\partial v}{\partial z }\right)+v_{s}S,\]  
where \(x\), \(y\), and \(z\) are the Cartesian coordinates, and \(u\), \(v\), and \(w\) are the velocity components along the \(x\), \(y\), and \(z\) directions, respectively; \(S\) is the magnitude of the discharge from point sources, and \(u_{s}\) and \(v_{s}\) are the velocities at which the water is discharged into the ambient water; \(\eta\) is the surface elevation; \(d\) is the still water depth; \(h=\eta+d\) is the total water depth; \(f\) is the Coriolis parameter; \(g\) is the gravitational acceleration; \(\rho\) is the density of water, and \(\rho_{0}\) is the reference density of water; \(s_{xx}\), \(s_{xy}\), \(s_{yx}\), and \(s_{yy}\) are components of the radiation stress tensor; \(p_{a}\) is the atmospheric pressure; \(v_{t}\) is the vertical turbulent (or eddy) viscosity; and \(F_{u}\) and \(F_{v}\) are the horizontal stress terms. In the MIKE 3 FM model, the free surface is taken into account using a sigma-coordinate transformation approach. Discretization in the solution domain is performed using a finite volume method. Spatial discretization of the primitive equations is performed using a cell-centered finite volume method. In the horizontal plane, an unstructured grid is used while in the vertical direction, the discretization is structured [41]. The Coriolis and wind force are neglected for small scale physical model in present work. Simulation Setup of Experiments by [PERSON] and [PERSON] [30]  
For the MIKE 3 FM model, the simulations are conducted with mesh resolutions of 0.15, 0.1, 0.05, and 0.01 m corresponding to 120, 267, 1068, and 26,700 elements; the results of the mesh sensitivity analysis for all the grids are shown in Figure 5, indicating that the grid size of 0.05 m is suitable for the purpose of this study. A suitable grid size and time step lead to better fitting and predicted precision and a faster convergence speed. In the subsequent numerical computations, uniform grid systems with a minimum guide spacing of 0.05 m, the time step of 0.01 s and 4000 time steps are applied so that the Courant-Friedrich-Levy (CFL) condition is sufficient to guarantee stability and satisfactory accuracy for the model.