## 4 Partitioned Strong Coupling Formulation
Moreover, a higher-solidity net (i.e., \(Sn=0.33\)) forms wake structures with more elongated shear layers. Figure 13c,d show that vortices in the top sections of the net panel develop faster than those in the bottom sections, especially when the Reynolds number is higher than 1200. This is because, aside from the shielding effect, as the Reynolds number increases, the separated shear layers in top sections become more unstable. The transition of the shear layers and shear-layer vortices produces increased near-wake vortices, which leads to the breakdown of the vortices in both the shear layers and the near wake. Compared to vortices in the middle and bottom sections of the net panel, the energy loss induced by vortex interactions generates smaller vortices in the top sections. Furthermore, when \(Sn=0.33\), the shear layer attachment seems to be suppressed due to the vortex interactions. This is consistent with the two-dimensional demonstrations in Figure 3:1 These unstable shear layers and the delay of vortex shedding also contribute to the drag reduction. Figure 3:2 Three-dimensional instantaneous vorticity structures behind the flexible net panels at the angles of attack between \(\pi/3\) and \(\pi/2\): (**a–c**) \(Sn=0.16\); (**d–f**) \(Sn=0.33\). ## 7 Conclusions

This paper proposes a coupled fluid-structure partitioned scheme to study the FSI of flexible net panels under steady flow. Using the FVM and FEM schemes, the coupled fluid-structure equations are solved separately in the fluid and solid subdomains. An arbitrary Lagrangian-Eulerian formulation is employed to accommodate the independent mesh motion at each time step. Then, the Dirichlet boundary conditions for the fluid and Neumann boundary conditions for the structure are imposed along the interface. Considering this, the variables, namely the forces, are transferred along the interface via a predictor-corrector scheme. Two net panels with different solidities are examined based on the present coupled fluid-structure partitioned scheme. The results show that both the drag coefficient and the velocity reduction increase alongside the net solidity, but they decrease as the Reynolds number/attack angle increases. When the solidity \(S_{n}\) equals 0.16, the relative difference in the drag coefficient between the present numerical simulations and analytical predictions is approximately 15%. When the solidity \(S_{n}\) is 0.33, compared to the validated analytical model, the average difference is about 4.2% at \(Re<1500\). Hence, the present numerical model predicts the drag coefficient reasonably well. Greater velocity reduction exists at \(Re<600\), while moderate velocity reduction appears at \(600<Re<1500\). The average values for these two nets are 7.5% and 12% regarding \(Sn=0.16\) and \(Sn=0.33\). The velocity distributions along the \(y\)-direction at different distances show distinct patterns: those in the middle of near field and far field are more stable. Severe velocity fluctuations have been observed in the near field when \(Sn=0.16\). This could be caused by the instability of the

Figure 3:3 Three-dimensional instantaneous vorticity structures behind the flexible net panels at angles of attack between \(\pi/4\) and \(\pi/3\): (**a**,**b**) \(Sn=0.16\); (**c**,**d**) \(Sn=0.33\). free shear layers. Moreover, in terms of the near-wake vortex distribution, the low-solidity net favors forming vortices in the shear layers and the wake, while the high-solidity net prefers the wake rather than the shear layers. The non-dimensional recirculation width (\(W_{r}^{*}\)) is dependent on the solidity, the Reynolds number, and the angle of attack. When the net solidity \(Sn\geq 0.33\), the flow shows that the wake interactions and the shear layers have been disturbed. However, the wake structures behind the net panel have more elongated shear layers, and vertical net twines have a predominant effect on vortex formation. Conceptualization, L.X. and Z.X. ; methodology, L.X. and Z.X. ; software, H.Q. and P.L. ; validation, L.X., H.Q. and P.L.