## 2 Materials and Methods
### FE Modelling and Study Cases
Here X, Y and Z directions were in-line flow direction, cross flow direction and depth direction, respectively. Large eddy simulation (LES) with bounded second order implicit transient formulation was selected as the mathematical model for turbulence in computational fluid dynamics (CFD), which reduced the computational cost with acceptable accuracy. The flow properties, such as flow density, kinematic viscosity coefficient and flow velocity listed in Table 5 were inputted in this module. The inlet, outlet, left, right, top and bottom sides were defined as the boundary conditions of velocity inlet, outflow, symmetry and wall, respectively. To achieve the data transfer between Transient Structural and Fluid Flow, i.e., the two-way fluid structure interaction (FSI), module of System Coupling was utilized, and the simulation time (80 s) and step size (0.2 s) were set in this module. The fluid grid of 5D \(\times\) 5D area around the riser was refined and set as the dynamic mesh zone with smoothing and re-meshing methods. Based on the results of convergence study, there were 1.15 million elements in the refined zone and 0.52 million elements for the other flow area, i.e., 1.67 million elements in total were employed in the flow zone. For the risers, 300 elements in axial direction and 20 elements in hoop direction were employed. In the though-thickness direction, one element, 22 elements and 18 elements for risers 1, 2 and 3, respectively. Note that, the laminate data were transferred from ACP (Pre) to Transient Structural and the number of elements in though-thickness direction was set as the number of layers of the structure automatically. In total, there were 6000 elements, 132,000 elements and 108,000 elements for risers 1, 2 and 3 respectively. Figure 4: _Cont._  
In this study, a tension was applied to the riser's top to keep its vertical position and the gravity, buoyancy and current load were also employed. The tension forces were set as 1.5 and 2 times the structural weight of steel and composite risers, respectively. The gravity and buoyancy loads were determined by the geometry of each riser. The current data of the Gulf of Mexico [2,14] was utilized according to the API Recommended Practice [49], which were 0.36 m/s for a 1-year winter storm, 1.22 m/s for a 100-year hurricane and 2.13 m/s for a 100-year loop current conditions. In the Gulf of Mexico, the sea water density is 1024 kg/m\({}^{3}\) and the kinematic viscosity coefficient \(\upsilon\) is 1.06 \(\times\) 10\({}^{-6}\). Table 5 shows the different cases in this study. Reynolds numbers for all the study cases were determined by Equation (1), where U is the flow velocity, D is the outside diameter of the riser, \(\upsilon\) is kinematic viscosity coefficient. Turbulent intensity employed were calculated by Equation (2), where I is turbulent intensity and Re is Reynolds number. \[\text{Re}=\frac{\text{UD}}{\upsilon} \tag{1}\]  
\[\text{I}=0.16\text{Re}^{(-1/8)} \tag{2}\]  
From Table 5, it is clear that the top-tension forces required for composite risers were much smaller than that of the steel riser, although the tension force ratios of composite risers were larger (1.5 and 2  
Figure 4: FE models for (**a**) flow zone and (**b**) steel and FRP composite risers.