# Numerical Modelling of a Floating Wind Turbine Semi-Submersible Platform
## 2 Materials and Methods
### Mesh  
#### 2.2.1 Mesh Domain  
The computational domain is a semi-cylinder with a diameter of 5 times the hydrodynamic diameter of the platform (D\({}_{\rm H}\)) and a height of 10 times the height of the device. These dimensions are sufficiently large to avoid the effect of wave reflection due to the curved walls while maintaining the same depth as the one used in the experimental runs. The volume is differentiated in two main meshes. The background mesh, which embraces the whole volume of study, and the overset mesh, which is focused on the movement of the platform and the behaviour of the fluid alongside it, has variable cell size depending on the area covered.  
In the background mesh, five different areas can be distinguished. In four of them, the cell size is defined using the trimmer anisotropic function, which allows us to modify the cell dimensions in all three axes. The area where the cells are not modified is that corresponding to the air, the one that is not numbered in Figure 1, and that is because it is the least important area for this analysis; therefore, it has the largest cells of the volume of study.  
The other 4 areas are defined to have a better understanding of them. Area 1 is the free surface area, which has the smallest cells of the background mesh. The cells' area is defined considering the wavelength, obtained by the heave natural period of the platform, and then the Z dimension is defined by using an aspect ratio (AR) of 4, which is  
Figure 1: Section with the different sub-volumes used in the background mesh (**top**) and the general volume of study (**mid**) and details of the geometry simulated (**bottom**).  
defined in Equation (11). Both horizontal axes, x and y, have the same dimensions in the whole volume.  
\[AR=\frac{\Delta\mathrm{z}}{\Delta\mathrm{x}} \tag{11}\]  
Area 2, the under-free-surface refinement space, is refined to not lose energy of the waves in that area formed due to the movement of the platform. The \(AR\) is maintained in all volumes. The length of its cells in the x and y axes is twice that in the free surface.  
The deep-water area, Area 3 in Figure 1, has the same size in the horizontal axes as the air area. The last zone, called the column and defined as Area 4, has the same cell size as the free surface one. This area is created to optimize the data transfer between the overset mesh and the background mesh, and to try to avoid any problems in the mesh definition due to cell size differentiation, which could lead to the breaking of the simulation.  
In the background mesh, three types of boundaries can be identified. The top of the volume (the orange face in Figure 1) is defined as a pressure outlet area, which allows the air to flow freely. The curved and bottom boundaries are defined as walls with a non-slip condition, while the vertical boundary in the XZ plane is defined as a symmetry plane, which allows us to only study half of the platform.  
This last boundary has an important effect in the reduction of the computational cost of the simulations. However, it only allows us to study three degrees of freedom (DoFs), namely, heave, surge and pitch.  
The overset mesh has two different areas: the free surface area, which is designed to cover the free surface interacting with the platform, and the background. Due to this, the free surface area of the overset mesh will be higher than the free surface area of the background mesh. On the contrary, the cell size of it will be much smaller, with its dimensions being 60% smaller than those of the free surface area of the background mesh. The rest of the overset has the same cell size as the cells in Area 4 of the background mesh. Moreover, a prism layer condition is applied around the platform. With a total width of 5 mm and 13 layers with a growth coefficient of 1.2, it ensures that we do not have a value of wall y+ higher than 1.5.