## 3 Development of Numerical Models  
Two numerical models of the monopile foundation are developed in this section. The first model is for investigating the effectiveness of \"fishnet\" in erosion reduction, which is intuitively indicated by streamline, seabed surface shear stress, and eddy viscosity. The second is for optimizing the design of \"fishnet\" technology. As Figure 3 shows, the parameters being optimized included the size of fishnet (\(l\)), the diameter of the fishnet thread (\(d\)), and the length of the fishnet device (\(H\)). In the numerical calculations, a monopile foundation with a diameter of 7 m was considered, which was used to support a VESTAS 8-MW offshore wind turbine. The flow speed \(\overline{U}\) was assumed to satisfy the following profile [23]:  
\[U(z)=\left\{ \begin{array}{ll}\big{(}\frac{z}{0.32\,h}\big{)}^{\frac{1}{2}} \overline{U}&(0<z<0.5h)\\ 1.07\overline{U}&(0.5h<z<h)\end{array} \right., \tag{1}\]  
where \(z\) refers to the distance above the seabed, \(h\) indicates the water depth, and \(\overline{U}\) is the depth average flow speed. The current speed profile shown in Equation (1) was used to determine the input current based on the current speed of 0.7 m/s at the height of 0.32 \(h\) above the seabed [23]. Subsequently, a numerical model was developed in ANSYS FLUENT [24] to simulate the monopile foundation of an offshore wind turbine. As shown in Figure 4, a 220-m-long, 60-m-wide, and 30-m-high fluid domain was defined. The coordinates of the bottom of the center of the pile were (0, 0, 0), and the positive direction of the \(X\)-axis was the water flow direction. In general, more meshes in a numerical simulation generate more accurate calculation results and, correspondingly, longer calculation times. In order to obtain accurate calculation results in a shorter calculation time when the iteration time was set to 2500, the correlation between the number of meshes  
Figure 4: Fluid domain in the numerical model: (**a**) isometric view; (**b**) rearview. Figure 3: A numerical model of the monopile: (**a**) main view; (**b**) geometries of the fishnet. and the calculation results of the maximum shear stress on nearby seabed surface was calculated first. The calculation results are shown in Figure 5.  
From Figure 5, it can be seen that the maximum shear stress showed a positive correlation with the number of elements and started to converge to a relatively steady value after the number of elements was larger than 14.49 million. Therefore, the fluid domain was discretized by using 14.49 million mesh elements in the subsequent numerical calculations. The specific settings are shown in Table 1.  
When setting the number of elements to 14.49 million, the fluid domain in Figure 4 was meshed, and the meshing results are shown in Figure 6. In order to accurately describe the water behavior around the \"monopile foundation\" and its influence on the scour pit while without causing excessive calculation, fine meshes were only adopted to discretize the fluid domain in the vicinity (60 x 60 m) of the monopile and a 14-m-wide region before and after the monopile. The fluid domain in other regions was discretized using coarse meshes. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Setting** \\ \hline Size function & Curvature \\ Initial size seed & Active assembly \\ Smoothing & Medium \\ Transition & Slow \\ Span angle center & Fine \\ Curvature normal angle & 12\({}^{\circ}\) \\ Min size & 0.02 m \\ Max face size & 4 m \\ Max Tet size & 4 m \\ Growth rate & Default (1.20) \\ Use automatic inflation & Program controlled \\ Inflation option & First aspect ratio \\ Fir aspect ratio & 5 \\ Maximum layers & 5 \\ Triangle surface mesher & Program controlled \\ Topology checking & Yes \\ Pinch tolerance & Default (\(4.5\times 10^{-3}\) m) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Settings for meshing the fluid domain of interest. Figure 5: Effect of the number of mesh elements on the Fluent 17.0 calculation results.