## 2 Risers' Geometries and Materials and FE Modeling
### FE Modeling  
The simulation of risers' VIV was achieved by ANSYS17.0 including modules of Geometry, ACP, Transient Structural, Fluid Flow and System Coupling (Figure 2). The following geometry was utilized to create the basic geometry of flow field: 10D \(\times\) 20D for 2D simulation and 10D \(\times\) 20D \(\times\) 12.5 m for 3D simulation. The basic geometry of the risers were based on previous design results [6; 7; 10; 13]. Flow situation was simulated by Fluid Flow (Fluent) including flow dimension, flow model, flow properties, flow boundary conditions, etc. The surface size of the flow field is defined by 10D \(\times\) 20D, where D is the outside diameter of the risers. The riser center is 5D from the inlet. One-year winter storm situation in Gulf of Mexico [36], i.e., velocity \(U\) = 0.36 m/s and kinematic viscosity coefficient \(v\) = 1.06 \(\times\) 10\({}^{-6}\), was used as the design velocity in this paper. Large eddy simulation (LES) which allows the largest and most important scales of the turbulence to be resolved (small eddies are modeled), while greatly reducing the computational cost incurred by the smallest scales, was selected for the CFD simulation. Resolving only the large eddies allows larger time-step and coarser mesh sizes than direct numerical simulation (DNS). However, LES still requires finer meshes than Reynolds Averaged Navier-Stokes (RANS). Meanwhile, LES has to be run for a sufficiently long flow-time to obtain stable statistics of the flow. As a result, the computational cost (memory and CPU time) involved with LES is normally higher than that in RANS calculations. The inlet, outlet, left and right sides and top and bottom sides were defined as boundary conditions of velocity inlet, outflow, symmetry and wall, respectively. More specifically, velocity inlet consisted of 0.36 m/s (all three risers) for velocity magnitude; 3.78% (Riser 1), 3.75% (Riser 2), and 3.77% (Riser 3) for turbulent intensity (Equation (7)); O.D. of each riser for hydraulic diameter; 1.0 was utilized for flow rate weight in outflow boundary; symmetry boundaries were used for the left and right sides to reduce the extent of  
Figure 2: Flow chart of vortex induced vibration (VIV) simulation with two-way fluid–structure interaction for FRP composite riser. computational resource; in the wall boundary, stationary wall was used for wall motion and no slip for shear condition. To use LES model, bounded second order implicit transient formulation must be chosen as solution method. \[I=0.16\sqrt[-1/8]{Re} \tag{7}\]  
where \(I\) is turbulent intensity and \(Re\) is Reynolds numbers. ACP (Pre) was utilized to create the lamination of composite risers (Tables 1 and 2) including material properties for liner and composites, liner and composite lamina thicknesses, fiber orientation, numbers of reinforced layers, and laminate stacking sequences (Figure 3) for the layered-structure method. Transient Structural was utilized to simulate the dynamic response of risers including displacement history, global stress distribution, etc. Besides the geometry of the riser, the input parameters also included the gravity, top-tension force (Table 4), buoyancy (based on the geometry of the riser and the density of the fluid), simple support at the top end, fixed support at the bottom end and the fluid solid interface. ACP (Post) was utilized to present the dynamic stress and deformation response for each lamina of the composite risers for the layered-structure method. System Coupling was utilized to transfer the data between Transient Structural and Fluid Flow to achieve the two-way fluid structure interaction. In this module, analysis type was set as transient and the duration time was set as 200 s (step size is 0.2 s). For the Co-Sim. Sequence, Fluid Flow (Fluent) was \(1\) and Transient Structural was \(2\). Table 4 presents the flow situation and Reynolds numbers (\(Re\)) and the tension forces for all the risers.