## 2 Methodology
### Coupling of Fluid and Structure  
The wind flow results in nodal forces on the surface mesh of the structure, typical for the numerical approach (CFD) at hand. These fluid forces need to be transferred to the  
Figure 2: Main assumptions and parameters of the structural model. structural model (modeled using computational structural mechanics--CSM methods) in a conservative way, referring to the conservation of forces in an integral sense. Thus, the resulting forces on the surface mesh on the fluid solver side need to be the same as the acting forces on the structure during the CSM simulation. These data transfer operations can be generically seen as a mapping operation. It needs to be noted that the deformations of the structural model are not sent back to the fluid solver; as such, the wind flow CWE model acts as if we were only able to see the rigid structure throughout the total duration of the simulation. This manner of assessing and transferring fluid forces is typical to either HFPI techniques (on a rigid model) or CFD simulations and leads to a one-way coupled fluid-structure interaction (FSI) approach, which means that only the wind flow affects the structure (due to arising forces), but structural deformations (kinematics) do not have an influence on the geometry of the flow domain considered. The main goal is to identify the minimum amount of considered structural detailing (represented here by the minimum amount of finite elements in discretization and/or number of mode shapes used for modal reduction), which leads only to a minimal degree of variation from the full resolution model. The minimum (or acceptable) level of refinement is established based on intended applications. The EOM in spatial coordinates is displayed in Equation (3), where \(x(t)\) denotes the vector of the DoFs of the generalized displacement, with time derivatives also being marked. The matrices \([M]\), \([B]\), and \([K]\) represent mass (consistent), stiffness, and damping (Rayleigh), respectively. The corresponding vector of external forces is represented by \(\{F(t)\}\). The sizes of the matrices and vectors are shown using the number of DoFs \(n\). Generalized discrete EOM. \[[M]_{n\times n}\{\ddot{x}(t)\}_{n\times 1}+[B]_{n\times n}\{\dot{x}(t)\}_{n \times 1}+[K]_{n\times n}\{x(t)\}_{n\times 1}=\{F(t)\}_{n\times 1} \tag{3}\]  
Transformation into modal coordinates. The eigenvalue problem for the conservative (undamped) structure is  
\[[K]_{n\times n}[\Phi]_{n\times n}=[M]_{n\times n}[\Phi]_{n\times n}[\Lambda]_{ n\times n} \tag{4}\]  
where \([\Phi]_{n\times n}=[\{\phi_{1}\}_{n\times 1}\{\phi_{2}\}_{n\times 1},\ldots, \{\phi_{n}\}_{n\times 1}]_{n}^{T}\) is the modal matrix, consisting of \(n\) modal vectors; \([\Lambda]_{n\times n}=[diag\{\lambda_{1},\lambda_{2},\ldots,\lambda_{n}\}]_{ n\times n}\) is the modal stiffness matrix, with \(\lambda_{i}=\omega_{i}^{2}\) for \(i=1,n\), consisting of \(n\) eigenvalues on the main diagonal. This assumption should be well accepted for civil engineering structures, which are typically highly underdamped. Mass-normalization is used for obtaining the modal matrix \([\Phi]_{n\times n}\), such that  
\[[\Phi]_{n\times n}^{T}[M]_{n\times n}[\Phi]_{n\times n} =[I]=[\overline{M}]_{n\times n} \tag{5}\] \[[\Phi]_{n\times n}^{T}[K]_{n\times n}[\Phi]_{n\times n} =[\Lambda]=[\overline{K}]_{n\times n}\] \[[\Phi]_{n\times n}^{T}[B]_{n\times n}[\Phi]_{n\times n} =[\mathbb{B}]=[\overline{B}]_{n\times n}\]  
where \([\mathbb{B}]_{n\times n}=[diag\{\beta_{1},\beta_{2},\ldots,\beta_{n}\}]_{n \times n}\) is the modal damping matrix, with \(\beta_{i}=2\zeta_{i}\omega_{i}\) for \(i=1,n\), \(\zeta_{i}\) being the damping ratio for the \(i\)-th mode.