## 3 Results and Comparison
### Results for 3D VIV with FSI Using Different Modeling Methods  
The 3D CFD simulation with FSI is adopted for the VIV of all the risers. For Riser 1 (steel riser), monolithic model is utilized and for Risers 2 and 3 (composite risers), two different modeling methods, i.e., effective modulus method (EMM) and layered-structure method (LSM) are employed. The displacement time history of all three types of risers are plotted in Figure 11 for three typical location, which are 1.2 m, 6.2 m and 11.2 m below the water surface. More specifically, Figure 11a-c shows the displacement time history at \(-1.2\) m for Risers 1, 2 and 3, respectively; Figure 11d-f shows the displacement time history at \(-6.2\) m for Risers 1, 2 and 3, respectively; and Figure 11g-i shows the displacement time history at \(-11.2\) m for Risers 1, 2 and 3, respectively. Figure 11: _Cont._  
Figure 10: Vorticity for different times: (a) \(t=0.4\) s; (b) \(t=8\) s; and (c) \(t=14\) s.  
Figure 12 plots the maximum cross-flow displacement of the risers with different modeling methods. In Figures 11 and 12, it is found that:  
Figure 11: Displacement time history of the risers for the vortex-induced vibration. (**a–c**) shows the displacement time history at \(-1.2\) m for Risers 1, 2 and 3, respectively; (**d–f**) shows the displacement time history at \(-6.2\) m for Risers 1, 2 and 3, respectively; (**g–i**) shows the displacement time history at \(-11.2\) m for Risers 1, 2 and 3, respectively. Figure 12: Maximum cross-flow displacement of the risers with different modeling methods. For the same riser: (i) different modeling methods lead to similar results for riser's displacement time history; (ii) the deformation in the middle part of the riser is larger than that in both ends, and the deformation close to the fixed end is the minimum; (iii) the deformation in the flow-direction is relatively stable at a specific value while the deformation in the cross-flow direction increases and decreases periodically; and (iv) the vibration in cross-flow direction is more obvious than that in flow direction. 2. For the different risers, Riser 1's displacement is less than Riser 2's displacement, which is less than Riser 3's displacement, due to their different bending modulus and tension forces. The time history of displacement for all the risers in flow direction is quite different from that in cross-flow direction, that is, the flow-direction displacement will maintain at a relatively stable value and vibrate slightly after the initial growth. Figure 13 illustrate the maximum displacement of the risers in flow-direction for all the risers with different modeling methods. Figure 13a shows the maximum flow-direction displacement for Riser 1; Figure 13b,c presents the maximum flow-direction displacement for Riser 2 with EMM and LSM, respectively; and Figure 13d,e illustrates the maximum flow-direction displacement for Riser 3 with EMM and LSM, respectively. Figure 13: Maximum flow-direction displacement of the risers with different modeling methods. (**a**) Shows the maximum flow-direction displacement for Riser 1; (**b**,**c**) presents the maximum flow-direction displacement for Riser 2 with EMM and LSM, respectively; (**d**,**e**) illustrates the maximum flow-direction displacement for Riser 3 with EMM and LSM, respectively. The flow-direction displacements are various for different risers: Riser 1's displacement < Riser 2's displacement < Riser 3's displacement. For the same riser, EMM and LSM lead to the similar flow-direction displacement. Figures 14 and 15 show the maximum von Mises stress and the stress distribution diagram for the Risers 1, 2 (EMM) and 3 (EMM). In Figures 14 and 15, it is obvious that the maximum von Mises stress follows: Riser 1 > Riser 3 > Riser 2. This is not totally dependent on the risers' modulus.