Wind-Induced Response Assessment of CAARC Building Based on LBM and FSI Simulation

Abstract

It is very important for the wind-resistant design of high-rise buildings to assess wind-induced vibrations efficiently. The Lattice Boltzmann Method-based Large Eddy Simulation and Fluid–Structure Interaction techniques are used to identify the surface wind pressure and wind-induced dynamic response of a CAARC standard high-rise building. Compared with wind tunnel tests, a detailed analysis of the accuracy of simulated wind pressures and base moments of the CAARC model are discussed under multiple wind direction angles. The differences between one-way and two-way Fluid–Structure Interaction simulations are compared under two different reduced wind velocities. The research results show that the simulated mean surface wind pressures of building under seven wind direction conditions have an error within 15% compared to probe measurements, and the average and root mean square base bending moments agree well with the wind tunnel tests. The top transverse wind-induced vibrations of the buildings are significantly larger when the reduced wind velocity reaches 4.6, indicating that aerodynamic damping effects on structural responses should not be overlooked. The research findings of this article provide valuable technical references for the application of LBM methods in the wind load effect assessments of high-rise buildings.

1. Introduction

In the context of frequent extreme weather events and high-density urban development, the slender structures and extreme wind climate of high-rise buildings make them more prone to overall or local structural wind-induced vibrations, which can affect both structural safety and occupant comfort. Therefore, it is crucial to assess the vibration characteristics of high-rise building structures under lateral wind loads for building design.

Physical wind tunnel tests are generally the standard means for wind load assessment in practical engineering projects. Considering the costs and testing periods, however, wind tunnel tests are difficult to directly apply to the iterative design in the preliminary stage. Additionally, scaled aerodynamic models fail to fully consider the Fluid–Structure Interaction phenomenon in high-rise buildings, making architects cautious when considering typhoons or hurricanes. With the increasing maturity of computational fluid dynamics (CFD) methods and abundant server-based parallel computing resources, the construction industry has attempted to use CFD for building shape optimization in the design stage. Predicting surface wind pressure and the wind-induced vibration of the targeted building in a computer system allows for the rapid evaluation and optimization of reasonable building shapes and structural layouts in the preliminary design stage.

Large Eddy Simulation (LES), technology based on the finite volume method (FVM), is currently used to predict surface wind pressure and the wind-induced response of high-rise buildings in the field of structural wind engineering. To address the issues of accuracy and reliability of LES, many numerical simulation validation studies based on the Commonwealth Advisory Aeronautical Research Council (CAARC) standard tall building were conducted. These studies often involve wind pressure comparison and structural vibration analysis with wind tunnel test results. Compared to the Reynolds-averaged Navier–Stokes (RANS) model [1], LES can solve the turbulent flow field characteristics around the building and predict the distribution of mean and fluctuating wind pressure on the building surface, so that it can provide a more accurate time-series wind load for structural wind-induced response. Zheng [2] compared RANS and LES methods in simulating the effects of building facade geometric details on the flow field and wind pressure. The results showed that the LES method can more accurately capture changes in wind pressure on the windward facade, while the RANS method predicts stronger flow field disturbances. To improve LES computational efficiency, Wijesooriyaa [3] proposed a hybrid RANS–LES solver for efficiently solving the effects of wind on non-standard geometric shapes of a 406 m slender tower. They analyzed the effects of different sub-grid scale models (SGS) on wind-induced structural vibrations and found that the WALE turbulence model can accurately handle near-surface turbulence features. These studies discussed above mainly focused on validating the accuracy of mean surface wind pressure, but limited investigation into surface fluctuating wind pressure. Recent research has shown that inflow turbulence generation affects the satisfied atmospheric boundary layer wind field characteristics and LES accuracy. Thordal [4] adopted LES to simulate surface wind pressure distributions on a CAARC building under the influence of surrounding buildings. By generating reasonable turbulence inlet conditions and grid mesh techniques, they were able to accurately predict both mean and fluctuating wind pressure features on the building surface, with overall mean errors of base forces and torques compared to wind tunnel tests below 15%. Lamberti [5] compared the effects of different incoming turbulence characteristics on fluctuating wind pressure simulation results. They analyzed factors such as incoming direction roughness length, turbulent kinetic energy, and turbulent integral length scales, and found that accurately quantifying the statistical characteristics of turbulent wind fields at building locations is crucial for structural wind load analysis, recommending consideration of uncertainty in inlet turbulence. Hu [6] adopted two different inlet turbulence generation methods (NSRFG and CDRFG) on the wake feature simulation of the CAARC model. They found that inlet turbulence has a significant impact on the distribution of surface fluctuating wind pressure, with NSRFG better to simulate non-Gaussian features of surface fluctuating wind pressure, providing a reference for selecting peak factor values for building envelope wind pressure evaluation. Additionally, Deng [7] also proposed a new artificial turbulence synthesis method to improve the accuracy of CAARC building surface fluctuating wind pressure simulations. They analyzed the atmospheric boundary layer spectral characteristics, temporal correlation, and spatial correlation. From recent LES research progress, it is clear that LES turbulence model selection, inlet turbulence generation, computational domain, and grid size can affect the accuracy of fluctuating wind loads prediction. There is still significant uncertainty in using LES, especially for complex grid meshing and city model parallel computing in practical engineering projects.

Another challenge of current LES is the calculation of dynamic wind-induced response, which involves considering the interaction between atmospheric flow fields and structural vibrations (Fluid–Structure Interaction, FSI). Hou and Frison [8,9] conducted research on CAARC multi-degree-of-freedom aeroelastic wind tunnel tests. However, there are problems in aeroelastic wind tunnel tests, such as high test cost and model scale. There are one-way and two-way FSI methods, according to the data transfer mechanisms. Regarding the two-way FSI, the surface wind pressure and structural dynamics of building using CFD and structural mechanical solvers are calculated simultaneously. The CFD wind pressure data is loaded into the finite element structural model in each simulation integration time step to calculate structural vibration displacement characteristics. Next, the structural deformation information is fed back to the CFD solver and affects the flow field calculation. The one-way FSI calculation principle is simpler and does not consider the influence of structural deformation on the CFD results of the building flow field, thus improving computational efficiency. Compared to one-way FSI, two-way FSI can consider the negative aerodynamic damping effect of high-rise buildings under strong wind vortex-induced vibrations. It can theoretically be equivalent to multi-degree of freedom aero-elastic model in physical wind tunnel tests. Braun [10] were the first to use two-way FSI technology to conduct numerical simulations of the aerodynamic and aerodynamic elastic behavior of the CAARC model. They compared surface wind pressure simulations and structural vibration characteristics under different incoming flow reduction wind speed conditions and found that two-way FSI could reproduce consistent average and root-mean-square displacement in the along-wind direction with wind tunnel experiments. However, only the uniform incoming wind conditions are considered and the influence of incoming turbulence intensity on crosswind displacement characteristics are not discussed. To improve the computational efficiency of two-way FSI, Huang [11] proposed a parallel FSI method based on socket parallel architecture for CAARC building models. They first integrated the surface wind pressure on each floor and then transmitted integral forces and moments from each floor to the finite element model, thereby improving FSI computational efficiency. Feng [12] conducted a two-way FSI of a kilometer-height building via ANSYS Workbench and compared structural dynamic responses with and without consideration of aerodynamic elasticity. Péntek [13] considered the additional mass damper’s influence on structural wind-induced displacement using an FSI method. Yan [14] proposed an efficient two-way FSI technique based on an equivalent concentrated mass system. By comparing with other FSI equivalent methods and aerodynamic elasticity test data, it was found that this method, combined with LES, can efficiently capture and simulate the vortex-induced resonance phenomenon of CAARC high-rise buildings. This method provides a relatively efficient two-way FSI simulation method for engineering applications. Given the high computational cost of two-way FSI, Hasama [15] proposed a one-way FSI method based on a multi-degree-of-freedom spring-mass structural simplified model. They found that the method can effectively simulate the displacement in both the along-wind and crosswind directions at the top of the building. Zhang [16] performed wind-induced vibration analysis on the CAARC model using a one-way FSI method and found that the average wind pressure results on the building surface agreed well with wind tunnel experiments, but the fluctuating wind pressures are easily affected by inflow turbulence. By artificially considering aerodynamic damping in the one-way FSI calculation, they were able to effectively simulate the crosswind displacement response under different wind speed conditions. Wijesooriya [17] established a spring-mass system structural model and an efficient one-way FSI boundary wind pressure data transfer mechanism, and they were able to meet the computational requirements under different wind speed conditions in practical engineering applications. It is evident from the above studies that two-way FSI can account for negative aerodynamic damping under the influence of vortex-induced resonance. However, due to the high computational cost, it is challenging to apply these techniques during the engineering design phase. On the other hand, simplified computational methods for one-way FSI generally fail to replicate complex modes of vibrations with acceptable levels of accuracy.

In recent years, the Lattice Boltzmann Method (LBM) has gradually gained attention in the field of wind engineering due to its high parallel computing efficiency and natural transient solving characteristics. Unlike traditional CFD codes based on FVM, the LBM is based on algorithms designed from particle collisions and kinetic energy theory, focusing on the solution of microscopic velocity distribution functions at the mesoscopic scale. The LBM computational framework easily enables large-scale parallel computing and has relative advantages in dealing with complex boundary conditions and grid mesh. Schröder [18] conducted an LBM case to validate the wind flow around a typical square block at low Reynolds numbers (Re 2000~8000), and found that the LBM can effectively simulate the flow separation around the building and the unsteady flow separation in the downstream wake region. Wang [19] also conducted an LBM validation study based on the flow field measurements of low Reynolds number square arrays. They analyzed the characteristics of turbulent wind fields around the building under different incoming wind directions and found that LBM with GPU-based large-scale computation can achieve real-time reliable simulations with millions of grid points. Han [20] conducted a detailed comparison between the LBM–LES and FVM–LES results of single rectangular buildings. They compared the LBM’s ability to resolve flow fields and its computational speed under different grid resolutions with the FVM method. The results showed that LBM has a higher computational efficiency and is eight times faster than the FVM method under the same computational setup. Camps [21] compared and validated the results of LBM and FVM simulations for flow around a single building. They found that both methods were able to correctly capture the typical flow field characteristics around the building. They also found that the LBM method, when implemented on a GPU parallel computing architecture, was able to achieve more efficient simulations. Due to this efficient simulation capability, the LBM method has been applied to large-scale simulations of urban building clusters for wind fields and pollutant diffusion [22,23,24,25]. Buffa [26] used the LBM–LES method to simulate and validate the surface wind pressure on a scaled model of a rectangular high-rise building. They conducted a detailed analysis of the influence of inflow turbulence conditions, wall functions, and grid resolutions on the simulation results. The results showed that the LBM method can reasonably simulate the average wind pressure distribution features on the building surface, but further validation is needed for the fluctuating wind pressure and wind-induced vibrations.

Based on the current research status, it can be surmised that the application research on structural wind load simulations based on LBM–LES is still in its infancy, and there is an urgent need to conduct validation analysis of wind pressure simulations and wind-induced vibrations. The innovation of this article lies in that it focuses on the LBM–LES surface wind pressure and base force simulations and validations for the CAARC standard high-rise building models in the field of wind engineering, and attempts to apply the LBM method to efficient FSI computation. The differences between one-way and two-way FSI results under different reduced wind velocity conditions are compared. This article discusses detailed information on the LBM building wind pressure simulation and computational costs, providing valuable references for the application of the LBM method in wind-resistant structure design.

The paper is organized as follows. Firstly, Section 2 introduces the methodology and principle used in this article, including the LBM, LES turbulence model, and FSI. Next, Section 3 details the wind tunnel tests and numerical model of the CAARC model. Section 4 introduces the simulated turbulent atmospheric boundary layer wind fields using LBM, the grid accuracy discussion, and wind fields around the building under multiple wind directions, and the mean wind pressure and base moment verification results are also discussed. Section 4 also details the one-way and two-way FSI results under two different reduced wind velocity conditions. Conclusions are given in Section 5.

2. Methodology

2.1. Lattice Boltzmann Method

The basic idea of the Lattice Boltzmann Method is the numerical representation of the discrete-velocity distribution function of molecules on a mesoscopic scale and the Navier–Stokes equations describing macroscopic fluid motion can be derived using the Chapman–Enskog analysis. The discrete-velocity distribution function f_i(x,t) in LBM is solved using a collision-streaming scheme:

$$f_i(x+c_i\Delta t,t+\Delta t)=f_i(x,t)+{\mathsf{\Omega }}_i(x,t)$$

(1)

where the subscript i in f_i refers to one of discrete set of velocities {c_i} of the particle in velocity space, x denotes the physical position in a square lattice and Δt is the time step representing the time resolution. The Bhatnagar–Gross–Krook (BGK) collision operator Ω_i is used as following:

$${\mathsf{\Omega }}_i(f)=-\frac{f_i-f_i^{eq}}{\tau }\Delta t$$

(2)

$$f_i^{eq}(x,t)=w_i\rho (1+\frac{u\cdot c_i}{c_s^2}+\frac{{(u\cdot c_i)}^2}{2c_s^4}-\frac{u\cdot u}{2c_s^2})$$

(3)

where f^eq is the equilibrium distribution function depending on the local quantities of density ρ and fluid velocity u only. τ specific to the relaxation time and w_i is the weight of the chosen velocity set c_i. c_s represents the isothermal model’s speed of sound.

The macroscopic physical quantities, such as fluid density ρ, velocity u, pressure p, and viscous stress tensor, can be calculated from Equations (4)–(6):

$$\rho (x,t)={\displaystyle \sum _i{f}_i(x,t)}$$

(4)

$$\rho u(x,t)={\displaystyle \sum _i{c}_i{f}_i(x,t)}$$

(5)

$$p=\rho c_s^2$$

(6)

$${\sigma }_{\alpha \beta }\approx -(1-\frac{\Delta t}{2\tau }){\displaystyle \sum _i{c}_{i\alpha }{c}_{i\beta }(f_i-f_i^{eq})}$$

(7)

where σ_αβ is the viscous stress tensor, and c_iα and c_iβ are the velocity vector sets of different spatial direction positions.

It should be noted that the numerical accuracy of LBM is related to the selection of particle velocity sets scheme {c_i, w_i} denoted usually as DdQq where d is the number of spatial dimensions the velocity set covers and q is the set’s number of velocities. The D3Q27 velocity sets scheme is adopted in this paper suitable for turbulence modelling.

2.2. Large Eddy Simulation and Turbulence Model

The Large-Eddy Simulation (LES) is typically used for turbulence modelling in LBM when considering unsteady flows, especially for high-Reynolds-number turbulence. The Wall-Adapting Local Eddy (WALE) sub-grid viscosity model is used in the LBM Large Eddy Simulation (LBM). The WALE model is formulated as follows:

$${\nu }_{\mathrm{sgs}}=(C_w\Delta {)}^2\frac{{(G_{\alpha \beta }^d{G}_{\alpha \beta }^d)}^{3/2}}{{(S_{\alpha \beta }{S}_{\alpha \beta })}^{5/2}+{(G_{\alpha \beta }^d{G}_{\alpha \beta }^d)}^{5/4}}$$

(8)

$$S_{\alpha \beta }=\frac{1}{2}(\frac{\partial u_{\alpha }}{\partial x_{\beta }}+\frac{\partial u_{\beta }}{\partial x_{\alpha }})$$

(9)

$$G_{\alpha \beta }^d=\frac{1}{2}(\frac{\partial u_k}{\partial x_{\alpha }}\frac{\partial u_{\beta }}{\partial x_k}+\frac{\partial u_k}{\partial x_{\beta }}\frac{\partial u_{\alpha }}{\partial x_k})-\frac{1}{3}{\delta }_{\alpha \beta }\frac{\partial u_k}{\partial x_{\gamma }}\frac{\partial u_{\gamma }}{\partial x_k}$$

(10)

where S_ij is the strain rate tensor of the resolved scale, u_i is the fluid velocity in the i-direction, Δ is the filter width and the constant C_w is typically 0.325. Once resolving the dynamic viscosity from WALE model, the relaxation time $\tau$ can be obtained through macroscopic behavior of kinematic shear viscosity determined from LBM:

$$\nu =c_s^2(\tau -\frac{\Delta t}{2})$$

(11)

Since the numerical solution of boundary-layer turbulent flow usually requires a high number of grid elements, especially for the square lattice structure, the wall function is adopted for modelling the near-wall boundary layer velocity. Considering a generalized wall function proposed [27], the adverse and favorable pressure gradients in boundary layer can be taken into account. The boundary layer velocity field can be computed through the velocity of first lattice near wall and y+.

2.3. Fluid–Structure Co-Simulation

For fluid–structure co-simulation, the transient dynamic analysis for the structure was solved via the basic equation of motion as given in Equation (12):

$$[M]\ddot{u}(t)+[C]\dot{u}(t)+[K]u(t)=F(t)$$

(12)

where [M], [C], and [K] are the mass, damping, and stiffness matrices of the structure, respectively. Furthermore, ü(t), $\dot{u}$(t), and u(t) are the acceleration, velocity, and displacement of the structure and F(t) is the wind induced load solved by CFD. In the ABAQUS transient structural, Newmark time integration method is used to solve the equation of motion at the discrete time points. For the one-way FSI method, pressures recorded in the fluid domain, acting on the building surface, were unidirectional mapped onto the structural domain. For two-way FSI method, bidirectional data exchange was established, which means wind loads were mapped onto structural domain, and displacements were mapped back to the CFD building surface. The lattice in XFlow can dynamically follow the new position of the deformed geometry every time step when two-way FSI is adopted.

In the two-way FSI method [28], the exchange and mapping of data between XFlow and ABAQUS with different time steps and meshes is managed using the ABAQUS co-simulation engine (CSE). To handle the difference in time step size, the CSE employs the Gauss–Seidel algorithm for synchronization, which involves a serial process where one solver lags behind the other solver, one coupling step at a time. Spatial interpolation is used for data mapping between different meshes. Notably, the data exchange and mapping require significant computational costs. While the two-way FSI method enables the consideration of structural deformation on the flow field, excessive computational consumption limits its practical application in engineering.

In the one-way FSI method, time-series wind pressures are obtained from computational fluid dynamics (CFD) results by placing probes at the center point of the building surface of each structural element. Once the CFD analysis is complete, these pressure time histories are applied to each structural element to perform structural transient analysis. The advantages of the one-way FSI method include computational efficiency and stability to adapt to various commercial solvers. To compare the calculation accuracy and computational consumption between the one-way and two-way FSI methods employed in this study, wind-induced vibration analysis was conducted on the CAARC model.

3. CAARC Standard Building

3.1. Experimental Wind Tunnel Test

To verify the reliability of building wind tunnel tests and numerical simulation techniques, often the CAARC standard high-rise building model is commonly used for wind load study in structural wind engineering, with a dimension of 30.48 m × 45.72 m × 182.88 m (D_x × D_y × H). Currently, multiple wind tunnel testing institutions have conducted wind tunnel tests on this model and have established a relatively uniform testing standard and a large amount of building wind pressure test results. Thus, the CAARC model is used for verifying the accuracy and precision of the LBM–LES method in this paper. For surface pressure measurement tests of the CAARC rigid model [29], the pressure measurement points at a height of 2/3H on the building are arranged and the position of measurement points and a diagram of multiple wind direction angles are depicted in Figure 1. The incoming wind is defined as perpendicular to the Front surface, where the 1–5 measurement points of the CAARC model are located, with a wind direction angle of 0°. By rotating the building model clockwise, different wind direction angles are set for the calculation conditions, gradually increasing from 0° to 90° with an interval of 15°.

In order to compare the wind pressure measurement results from different wind tunnel testing institutions, it is uniformly stipulated that the reference wind pressure is the wind pressure at the top height (H) position of the scaled model. The mean and standard deviation of pressure coefficients are computed as following:

$$C_{p\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}=\frac{P_{\mathrm{mean}}-P_0}{0.5\rho U_H^2}$$

(13)

$$C_{p\mathrm{s}\mathrm{t}\mathrm{d}}=\frac{P_{\mathrm{std}}-P_0}{0.5\rho U_H^2}$$

(14)

where C_pstd and C_pmean are the mean and fluctuating wind pressure coefficients, P_mean and P_std are the average and standard deviation value of the wind pressure measured at building surface test points, respectively. P₀ represents the static pressure at the reference height H in the direction of free flow, ρ is the air density, and U_H represents the wind speed at the reference height H in the direction of free flow.

Figure 2 summarizes the distribution of the mean wind pressure coefficients at 2/3 height of CAARC building under a 0-degree wind direction angle from different institutions [29]. It can be observed from Figure 2 that the mean wind pressure coefficients submitted by different institutions show a generally consistent trend, but the average deviation is as high as 15%, especially in the negative pressure areas on both sides and the back of the CAARC standard building. When comparing the results of the NPL and TJ-2 wind tunnel experiments at Tongji University, it is found that the absolute value of negative pressure simulated by NPL is significantly smaller. This may be attributed to the fact that the turbulence intensity of atmospheric wind field simulated by NPL is relatively low. In addition, differences in the model scaling ratios used by different institutions may also contribute to the deviations in wind pressure test results.

This article mainly refers to the wind pressure test results of the CAARC rigid model conducted at Tongji University in China [29]. The actual length of the wind tunnel test section is 15 m, the width is 3 m, and the height is 2.5 m. In the test, a passive method was used to simulate the flow field, with a tower turbulence generator and distributed rough elements used to simulate the velocity and turbulence intensity distribution of the atmospheric boundary layer. The model scale ratio was selected as 1/300, and the wind tunnel test blockage ratio was 1.3%. Given the limited research on the simulation of strong turbulence conditions at D-category roughness landscape according to the Chinese Load Code for Design of Building Structures [30], the LBM–LES simulation method was verified through the comparison with Tongji University’s TJ-2 wind tunnel experiments.

3.2. Numerical Model Based on LBM

An LBM numerical model based on XFlow software (version 2020x) was established for the CAARC standard rectangular building. The overall computational domain size is shown in Figure 3. The building model size is the same as the wind tunnel test, with a scale ratio of 1:300. Referencing the research by Wijesooriya (2021), the height of overall computational domain is 3 × H and the side boundaries located 3 × H away from the target building. The windward face of CAARC building is 3 × H away from the inlet boundary, while the leeward face of building is 10 × H from the outlet boundary to avoid the re-circulation phenomenon. The building model blockage rate is less than 3% and the computational requirements for general building numerical wind tunnels are satisfied.

The mesh generation strategy is mainly divided into three steps: background mesh generation of computational domain, building surface refinement, and refinement region mesh setting. The schematic diagram of building surface mesh generation is shown in Figure 4. Firstly, the basic grid size of global computational domain is set as 0.08 m (dx). Secondly, the near-wall refinement approach is adopted over building surface with a minimum grid size of 1/32 × dx set. The grid resolution within the computation domain is increased gradually from the building surface to the boundary of the computational domain by a factor of two, thus forming a multi-scale octree grid structure. Finally, a local cuboid region is set up for the more refined resolution of wind flow fields around buildings. A rectangular refinement region with the dimension of 4H × H × 1.2H (length × width × height) is used. Additionally, the grid is further refined with a grid size of 1/16 × dx = 0.005 m within a height range of 0.1 m to capture the near-wall turbulence flow around the building.

Regarding the boundary condition of computational domain, the symmetric boundary is selected for the two sides and top of domain and the free pressure-outflow boundary is selected for the outlet face. The non-equilibrium enhanced wall function is used for the CAARC standard building wall surface and the bottom of the computational domain. The LBM–LES computational domain employs a velocity inlet boundary condition and the mean wind speed and turbulence intensity profile are specified using the following formulas:

$$\frac{U(z)}{U_{\mathrm{g}}}={(\frac{z}{z_{\mathrm{g}}})}^{\alpha }$$

(15)

$$I_{\mathrm{u}}(z)=I_{10}\cdot {(\frac{z}{10})}^{-\alpha }$$

(16)

where U(z) and I_u(z) are the mean wind speed and turbulence intensity at height z, Z_g is the reference height (0.61 m), and the reference wind speed U_g is 12 m/s. According to the load code for building structures in China, the wind profile index α under D-category terrain is set to 0.3 and the nominal turbulence intensity I₁₀ at 10-m height is set to 39%.

For the LES turbulence model setup, the WALE Large Eddy Simulation turbulence model is used for transient calculations, with a model parameter C_w set to 0.325. The Reynolds number of the scale model is approximately 1 × 10⁵. Considering the incoming turbulence, an isotropic synthetic turbulence method [31] was employed in the inlet velocity boundary condition to generate the horizontal turbulence fluctuations that meet the prescribed turbulence integral scale and Karman empirical wind spectrum. According to turbulence integral scale recommendation formula in European code, the inlet turbulence fluctuations were set to satisfy a 1 m turbulence integral scale (corresponding to a full-scale 300 m). The atmospheric boundary layer wind field simulation and related parameter calibration were carried out based on the LBM solver XFlow. The mean wind speed profile and turbulence intensity profile were implanted via a function module.

3.3. Setup of Aeroelastic Analysis

The time history analysis for both the one-way and two-way FSI were conducted with the same structural model to assess the response of the CAARC. The dynamic parameter characteristics of the CAARC aeroelastic model, as referenced in Braun’s research [10], are summarized in

Table 1. Mechanical properties of the CAARC model for FSI.

Specific Mass (Kg/m3)	160
Natural frequency (Hz)	0.173
Young’s modulus (N/m2)	2.3 × 108
Poisson’s ratio	0.25
Damping ratio to critical	1%

. The structural model is composed of C3D8 solid elements, consisting of a total of 9150 elements, as depicted in Figure 5. The frequencies of the first five modes obtained from structural modal analysis are presented in

Table 2. First five levels of modal frequencies.

Vibration Mode	X	Y	Torsion	X	Y
Natural frequency (Hz)	0.17	0.25	0.89	0.99	1.30

.

The structural analysis was conducted in ABAQUS using an implicit dynamic step. For the one-way FSI model, a step frequency larger than ten times the natural frequency (0.173 Hz) of the structure was required to capture high-order vibrations. In contrast, the two-way FSI model was solved every 2 × 10⁻³ s (500 Hz) to maintain synchronization with the CFD simulation, with data stored at a frequency of 50 Hz. To facilitate comparison between the one-way and two-way FSI methods, a step size of 2 × 10⁻³ s was used for both analyses. The simulations for both types of FSI were run for a total flow time of 1800 s, with data recorded only during the last 1500 s to allow the simulations to stabilize during the initial 300 s. The chosen time step of 2 × 10⁻³ s was sufficient to achieve convergence.

The simulation was conducted on a high-performance computer (HPC) utilizing a single node with 128 cores and a processor base frequency of 2.6 GHz. For the one-way FSI, the computational time for the CFD simulation was completed in 40 clock hours. The CFD simulation recorded the pressure on the building surface at intervals of 2 × 10⁻² s (50 Hz) as a pressure file record. Each pressure record includes the location on the surface of the structure in terms of X, Y, Z coordinates and the corresponding pressure value. Therefore, for 1500 s of flow time, a total of 3200 pressure files were recorded and can be easily processed to generate pressure time history loads for the structural model. For the two-way FSI simulation, approximately 406 clock hours were required to complete two cases, which is a significantly higher computational consumption compared to the one-way FSI, as shown in

Table 3. Computational consumption on HPC.

Case	$\mathbf{One}\text{-}\mathbf{Way}\mathbf{FSI}{\mathit{U}}_{\mathit{g}}/\left(\mathit{n}{\mathit{D}}_{\mathit{x}}\right)=1.5$	Two-Way FSI ${\mathit{U}}_{\mathit{g}}/\left(\mathit{n}{\mathit{D}}_{\mathit{x}}\right)=1.5$	$\mathbf{One}\text{-}\mathbf{Way}\mathbf{FSI}{\mathit{U}}_{\mathit{g}}/\left(\mathit{n}{\mathit{D}}_{\mathit{x}}\right)=4.6$	Two-Way FSI ${\mathit{U}}_{\mathit{g}}/\left(\mathit{n}{\mathit{D}}_{\mathit{x}}\right)=4.6$
Clock hour	10.2	94	30.1	312

.

4. Result and Discussions

4.1. Free Stream Flow without Obstacle

To validate the accuracy and reliability of the boundary condition adopted, the atmospheric boundary layer turbulence wind fields are simulated firstly based on the empty computational domain without any obstacle. The mesh configuration of the computational domain is as described earlier in Section 3.2, with a total grid number of 2.88 million in the empty domain. The adapted time step for calculations was determined based on Courant number 1 and the simulation time of scaled model is set to 6 s, corresponding to 1800 s for the full scale model. Figure 6 shows the simulated mean velocity and turbulence intensity profiles at building-placed position from an empty domain. The profiles from the wind tunnel test and wind load code are also presented. It can be observed that the mean wind speed and turbulence intensity profiles simulated by LBM–LES match well with the patterns observed in wind tunnel experiments. However, the turbulence intensity profile simulated by LBM–LES is relatively smaller than the profile from wind load code. This may be attributed to the grid filtering effect in LES, where artificially generated incoming turbulence causes a certain degree of attenuation within the computational domain.

The simulated wind spectrum at different inflow positions at 2/3 height of the computational domain is shown in Figure 7. It shows that the LBM–LES simulated wind spectrum matches well with the commonly recommended wind spectrum in wind engineering, although the high-frequency components of the wind spectrum decay rapidly due to the grid filtering effect. In the later stage, the simulation accuracy of high-frequency wind speeds can be improved by increasing the grid resolution. Overall, LBM–LES adopted in the paper can reproduce the incoming wind field characteristics consistent with wind tunnel experiments reasonably.

4.2. Sensitivity Analysis for Grid Resolutions

Grid sensitivity analysis was performed based on three grid resolutions to investigate the mesh dependency of the LBM simulated results. The mesh parameters of three CFD grid model are listed in

Table 4. Parameter statistics of different LBM grid resolutions.

Parameters	Basic Grid	Coarse Grid	Fine Grid
Refined level	5	3	6
Basic size dx (m)	0.08	0.08	0.08
Smallest grid size (m)	1/32	1/8	1/64
Cell number	3,434,470	499,600	6,197,862
Maximum y+	90	334	58
Cores × hour time	1080	384	2688

. The basic grid of the building surface was refined five times (1/2⁵ × dx), and the coarse grid scheme was refined only three times, while the fine grid example was refined six times. The basic grid size dx was 0.08 m, and each refinement represented a reduction of half of the grid size in the vicinity of the building. The same turbulence solver setting parameters are used in three models.

The mean horizontal wind speed contours from three mesh models at 2/3 × H of CAARC building and middle vertical section are shown in Figure 8 and Figure 9. It can be observed from Figure 8 that both the basic and fine grid schemes replicated the phenomenon of wind speed acceleration in the two-side areas around the CAARC building, with vortex-induced backflow forming at the rear regions of building and shear layers separating near the building’s corners, while the coarse grid scheme failed to simulate this phenomenon.

As shown in Figure 9, both the basic grid and fine grid schemes successfully reproduced the reverse flow structure at the top of the building, while the coarse grid scheme failed to simulate this phenomenon. Furthermore, the cavity behind the building reproduced by coarse grid scheme had a tendency to move away from the walls of the building to a certain extent, while the latter two schemes showed a similar cavity phenomena. It was also found that the coarse grid scheme had a larger velocity recirculation zone and larger vortex scales at the rear of the building, while a smaller vortex scale resolved in other two grid schemes.

Figure 10 presents the normalized vertical-component wind speed contour around CAARC building from three different gird schemes. As can be seen from the figure, all three grid schemes were able to simulate the downwash effect of high-rise buildings, where high-speed airflow from the upper part of the building impacts the ground due to the uneven velocity pressure effect along the height of the building. Comparing the three grid simulation results, the basic grid simulation is consistent with the fine grid results.

The comparison of mean wind pressure coefficients from three grid resolutions under a 0-degree wind direction are given in Figure 11. The simulated mean wind pressure coefficients on the windward side of the building by three grid schemes are consistent with the wind tunnel test, but the coarse grid scheme significantly underestimates the negative wind pressure on the building’s two-side areas. The mean negative wind pressure coefficients simulated by the basic grid and fine grid are basically consistent with the TJ-2 wind tunnel test, indicating that the simulation results are not dependent on the grid resolution.

From the above analysis results, it can be concluded that the basic grid resolution scheme used can reasonably simulate the mean wind field distribution characteristics and wind pressure distribution around the CAARC high-rise building. Considering both computational efficiency and accuracy requirements, the same grid scheme will be adopted in subsequent simulation cases for other wind direction angles.

4.3. Mean Wind Fields under Multiple Wind Angles

The surface wind pressure distribution of rectangular buildings with different aspect ratios shows significant differences under varying wind directions. Therefore, it is necessary to conduct a wind flow analysis for multiple wind angles during the design stage of the building plan to determine the worst wind load effect. Figure 12 presents the normalized horizontal wind speed distribution characteristics around the CAARC high-rise building under different wind directions. It should be noted that the building flow field for the 0-degree wind direction condition is already given in Figure 8.

It can be observed from Figure 8b and Figure 12f that there is significant flow separation on both sides of the CAARC building under 0-degree and 90-degree wind directions. The flow separation occurs at the sharp edges on both sides of the building, and the separated flow does not reattach. A comparison of the flow fields in the wake region of the building under the two conditions further reveals that the range of the wake vortex in the 0-degree wind direction case is significantly larger. From 0- to 15-degree wind direction (see Figure 12a), the flow structures around the building becomes more complex, with asymmetric flow separation on both sides of the building and a larger re-circulation structure developing in the central area of the upper side of the building, indicating worse negative pressure conditions. It can also be found that the separation and reattachment phenomena around the building become more complex as the wind direction angle changes. A comparison of Figure 12d,e reveals that a local re-circulation and reattachment flow structure appears on the windward front of the long side of the CAARC building under a 75-degree wind direction, while there is no significant separation phenomenon under 60-degree wind direction. This indicates significant differences in wind pressure at this location, and often requires a more refined grid resolution scale for accurate wind flow simulation.

4.4. Mean Wind Pressure on Building Surface

Figure 13 presents the simulated mean wind pressure coefficient contour of the CAARC standard building model under different wind direction angle conditions. Comparing the mean wind pressure coefficient maps in Figure 13a with the particle image velocimetry test from Yu [32], the mean wind pressure distributions from LBM–LES are in good agreement with the data from the wind tunnel test, except that those on the sidewall from LBM–LES simulations are slightly larger than that from the wind tunnel test. As shown in Figure 13a, the simulated mean wind pressures on the building surface under 0 degrees exhibit a clearly symmetric distribution. The windward face is mainly subject to positive pressure, with a maximum wind pressure coefficient of 0.82. The negative pressure on both sides of the building is symmetrically distributed and reaches its most unfavorable condition, while the pressure on the back of the building is relatively small. Under the influence of a 90-degree wind direction (see Figure 13c), the left side (Side-Left) of the building is the actual windward face. The wind pressure on both the Front and Back faces of the building is mainly negative, with the maximum value occurring at a local position on the top of the building. The mean wind pressure on the actual leeward face, i.e., Side-Right, is relatively small. As shown in Figure 13b, the distribution of wind pressure on the building surface becomes more complex and uneven under a 45-degree wind direction. The symmetry of the wind pressure distribution on the building surface disappears, and the maximum average negative pressure occurs at the intersection edge between the Side-Right and Back faces.

Figure 14 further presents the contours of fluctuating wind pressure coefficients on the surface of the CAARC building under three wind direction angle calculation conditions (0, 45, and 90 degrees). Comparing the fluctuating wind pressure coefficient contour maps in Figure 14a with the experimental results of Yu [32], it can be seen that, although there are significant differences between the windward fluctuating wind pressure distribution simulated by LBM–LES and the wind tunnel test, the leeward and sidewall simulation results are relatively close to the experimental distribution, and the simulation error is smaller compared to the existing traditional finite volume method. As shown in Figure 14a, the simulated fluctuating wind pressure coefficients on the left and right sides of the CAARC standard building exhibit symmetric distribution, with the maximum value occurring in the lower part of the building’s leeward face. Under 45-degree and 90-degree wind directions, the symmetry is not obvious, and the fluctuating wind pressure distributions are influenced by the turbulence of the incoming flow and the building shape itself.

To verify the reliability of CAARC wind pressure simulation in detail, Figure 15 presents the simulated mean wind pressure coefficients at 2/3 height of the building under all wind direction conditions and a comparative analysis with the two different wind tunnel test results. As shown in the figure, LBM–LES can simulate the consistent distribution of wind pressure at the test points with the TJ-2 wind tunnel experiment, although there are slight deviations at individual test points (see Figure 15b,e). The possible reason causing errors is that the wind flow distributions at this location are more complex under 30-degree and 75-degree wind directions, and a more accurate solution requires a finer grid resolution. As shown in Figure 15a under a 15-degree wind direction, the CAARC building experiences the most unfavorable negative pressure situation, where LBM–LES can accurately solve. The mean wind pressure error of all probe points is below 5%. It should be noted that changes in wind direction often result in rapid changes in wind pressure at local edge positions of the building, as shown in Figure 15f from probe point 15 to point 16, where LBM–LES simulates this change feature relatively well.

Considering that the turbulence intensity of the NPL wind tunnel test was relatively low, resulting in a smaller simulated mean wind pressure, while the LBM–LES and TJ-2 wind tunnel tests showed good agreement, further comparisons were made based on the TJ-2 results. The maximum and minimum mean wind pressure coefficients simulated by LBM–LES were then compared and summarized with the wind tunnel test results and given in

Table 5. Statistics of maximum and minimum mean wind pressure coefficients of test points under different wind direction angle conditions.

Wind Angle	Maximum Cp		Minimum Cp
	TJ-2	LBM-LES	TJ-2	LBM-LES
0°	0.84	0.82 (2%)	−0.81	−0.86 (6%)
15°	0.84	0.80 (5%)	−0.93	−1.00 (7%)
30°	0.81	0.77 (5%)	−0.50	−0.54 (8%)
45°	0.77	0.64 (16%)	−0.50	−0.47 (6%)
60°	0.82	0.80 (2%)	−0.50	−0.56 (12%)
75°	0.82	0.82 (0%)	−0.69	−0.59 (14%)
90°	0.86	0.79 (8%)	−0.77	−0.74 (4%)

. The relative error of the maximum wind pressure coefficient between LBM–LES simulation and TJ-2 wind tunnel test are generally within 15%, except for individual cases such as the CFD simulation result error being relatively large under a 45-degree wind direction.

It should be noted that for wind direction angles other than 0° and 90°, there is a noticeable non-fitted mesh problem on the building surface, which may affect the calculation results of wind pressure on the building surface. Although such problems can be improved by increasing the grid accuracy later, the computational cost will increase exponentially. At the same time, current research is developing new wall functions for atmospheric boundary layer wind field simulations to improve the accuracy of near-wall flow field simulations [33].

4.5. Wind-Induced Global Forces and Moments

Global force and base moment coefficients are defined as follows:

$$C_{\overline{M_i}}=\frac{\overline{M_i}}{0.5\rho U_H^2{H}^2{D}_y},C_{{\sigma }_{M_i}}=\frac{{\sigma }_{M_i}}{0.5\rho U_H^2{H}^2{D}_y}$$

(17)

$$C_{\overline{F_i}}=\frac{\overline{F_i}}{0.5\rho U_H^{2}H{D}_y},C_{{\sigma }_{F_i}}=\frac{{\sigma }_{F_i}}{0.5\rho U_H^{2}H{D}_y}$$

(18)

where i can take x, y, and z to represent global coordinate, $\overline{M_i}$ and ${\sigma }_{M_i}$ represent the mean and the standard deviation of base moments in i direction, and $\overline{F_i}$ and ${\sigma }_{F_i}$ are the mean and the standard deviation of global forces in i direction.

Taking the 0-degree wind angle case as an example, Figure 16 shows the time-series aerodynamic force and base moment coefficients of a CAARC building. It can be observed that building mainly experiences significant aerodynamic coefficients in the x direction and bending moment coefficients in the y direction, while the x-direction bending moment and y-direction aerodynamic forces fluctuate around zero, which is consistent with the periodical wake vortex phenomenon observed in the wind flows of CAARC building.

Figure 17 shows the mean and standard deviation of simulated base moments of a CAARC building in the x and y direction compared with wind tunnel tests. It can be seen from the figure that the simulated mean base bending moment coefficient under each wind direction angle shows a consistent trend with the wind tunnel test. The standard deviation of base moments of LBM–LES simulation exhibited slight larger than wind tunnel test. It should be noted that the isotropic turbulence boundary condition set at the inlet did not take into account variation characteristics of the integral turbulence scale consistent with the physical wind tunnel. This discrepancy may have introduced some level of error in the calculation of the fluctuating bending moment coefficient.

To quantitatively analyze the errors simulated by LBM–LES,

Table 6. Deviation statistics of LBM–LES simulation results compared with wind tunnel test base moment coefficients.

Wind Angle	CMx-mean		CMy-mean		CMx-rms		CMy-rms
	TJ-2	CFD	TJ-2	CFD	TJ-2	CFD	TJ-2	CFD
0°	0.00	0.00 (1%)	0.51	0.59 (16%)	0.11	0.14 (28%)	0.10	0.13 (34%)
15°	−0.06	−0.05 (14%)	0.49	0.47 (−4%)	0.08	0.06 (−21%)	0.08	0.12 (47%)
30°	0.07	0.15 (97%)	0.44	0.5 (14%)	0.05	0.06 (20%)	0.08	0.11 (42%)
45°	0.21	0.30 (42%)	0.39	0.34 (−11%)	0.05	0.07 (45%)	0.07	0.10 (45%)
60°	0.27	0.35 (26%)	0.28	0.32 (16%)	0.05	0.07 (35%)	0.07	0.09 (43%)
75°	0.28	0.32 (13%)	0.11	0.13 (15%)	0.06	0.08 (36%)	0.08	0.10 (22%)
90°	0.28	0.29 (3%)	0.02	0.00 (−93%)	0.06	0.08 (18%)	0.12	0.10 (−16%)

further summarizes the error results of the base bending moment simulated by LBM–LES relative to the TJ-2 wind tunnel experiment. The percentage in the table represents the relative errors. It can be seen that LBM–LES simulation results generally matched well with the experimental data of TJ-2 wind tunnel, while the X-direction mean bending moment coefficients are overestimated with an average relative error of 28.05%. At a 30-degree wind direction angle, the relative error of the simulated C_Mx is 97% compared to the TJ-2 experiment value of 0.07. The Y-direction mean bending moment coefficient has a relatively small error, except only a relative error of 93.46% at a 90-degree wind direction angle. When considering the standard deviation of bending moment coefficient, it can be seen that the simulated results of LBM–LES are generally overestimated, with significant differences in the Y-direction bending moment coefficient. Overall, this analysis demonstrates the effectiveness and reliability of LBM–LES in calculating building wind loads. The standard deviation of bending moment coefficient simulation results is significantly affected by the incoming turbulence fluctuations in the LBM model.

From the above analysis, it can be concluded that the LBM–LES method adopted are able to reasonably reproduce the surface wind pressure and base force characteristics of the CAARC standard high-rise building model. This provides an efficient simulation method for rapid wind load calculations and analysis in the early stages of practical engineering projects. Next, a further analysis of wind-induced structural vibrations will be conducted based on the XFlow-ABAQUS coupled method.

4.6. Wind-Induced Responses Based on FSI

The comparative aeroelastic analysis of the CAARC building model with experiment results using both one-way and two-way FSI method is the main subject of this section, which analyzes its structural response under two different reduced wind speed levels corresponding to the following reduced velocities—$U_g/\left(n{D}_x\right)$:1.5 (12 m/s), 4.6 (36 m/s). Figure 18 presents the time histories of longitudinal and transversal displacements computed at the top of the building for the different wind speeds simulated in the present aeroelastic analysis. Figure 19 displays the corresponding time histories of top-position acceleration. The average results of one-way coupling and two-way coupling simulations are close, except for transversal wind results at a reduced velocity of 4.6.

Mean and RMS structural responses obtained from the time histories of displacment shown in Figure 18 are normalized by the cross-section dimensions of the building model and compared with Melbourne [34] in

Table 7. Comparison of displacements of FSI results with wind tunnel tests.

Reduced Velocity and Case	Melbourne [34]	One-Way FSI	Two-Way FSI
1.5 $\overline{X}/D_x$	9.19 × 10−4	9.36 × 10−4	9.25 × 10−4
1.5 ${\sigma }_x/D_x$	2.16 × 10−4	4.31 × 10−4	3.76 × 10−4
1.5 ${\sigma }_y/D_x$	2.01 × 10−4	2.37 × 10−4	1.95 × 10−4
4.6 $\overline{X}/D_x$	8.27 × 10−3	8.39 × 10−3	7.63 × 10−3
4.6 ${\sigma }_x/D_x$	3.14 × 10−3	4.11 × 10−3	3.37 × 10−3
4.6 ${\sigma }_y/D_x$	3.21 × 10−3	3.52 × 10−3	7.16 × 10−3

. The mean wind normalized displacements obtained in the present work is well correlated with the experimental results at both wind speeds. The transversal RMS wind normalized displacements of one-way FIS and two-way FSI agree well with experimental results at a reduced velocity of 1.5, but RMS transversal wind normalized displacements at a reduced velocity of 4.6 obtained from two-way FSI simulation are larger than two times to the results of one-way FSI and experimental results. The reason for this difference is that the vortex shedding frequency under a reduced velocity of 4.6 is close to the natural frequency of the structure.

Figure 20 shows the power spectral density of the bending moment and aerodynamic correlation coefficients on the x and y directions of the base under a 0-degree wind direction angle. The periodic vortex shedding occurs in the wake region of the building model which is similar to square columns. Considering the effects of parameters from numerical simulations and wind tunnel tests [35,36], the Strouhal number for square columns is approximately between 0.12 and 0.16. The calculation formula for the Strouhal number St is defined as following:

$$St=\frac{nB}{U}.$$

(19)

where n represents the vortex shedding frequency, B represents the width of the building model, and U is the mean wind speed.

According to the theory related to vortex shedding, the peak frequency shown in Figure 20 is half of the conventional vortex shedding frequency. Therefore, it can be inferred that the vortex shedding frequencies under two reduced velocities in this article are 0.042 Hz and 0.13 Hz, respectively. The Strouhal numbers calculated under the full-scale model and the corresponding incoming wind speed are 0.16 and 0.165, respectively. The results are relatively close to the values of conventional square columns.

Conversely, the natural frequency of the CAARC structure in this paper is 0.17 Hz. Therefore, the vortex shedding frequency with a reduced velocity of 4.6 is closer to the natural frequency of the structure and closer to the frequency “locking” range, where vortex-induced resonance occurs. Thus, the obtained crosswind displacement fluctuations are more obvious.

Figure 21 compares the top node trajectories of CAARC standard buildings under the reduced velocities of 1.5 and 4.6. It can be seen that under a reduced velocity of 1.5, longitudinal vibration is the dominant factor. The top node trajectory calculated by one-way FSI and two-way FSI is very close, and the maximum full-scale displacement amplitude does not exceed 0.08 m. When the reduced velocity value becomes 4.6, the proportion of crosswind vibrations increase significantly. The vortex shedding frequency is closer to the natural frequency of the structure itself, resulting in a significant increase in the amplitude of crosswind vibrations, and the mode of wind-induced oscillations changes, with the maximum full-scale displacement reaching 0.6 m.

5. Conclusions

The LBM–LES and FSI techniques are adopted to predict wind load and wind-induced vibration of CAARC standard high-rise building model. The main conclusions are as follows:

(1)

The simulated probe mean wind pressures at 2/3 height of CAARC building matched well with the wind tunnel experiment under multiple wind angle direction. The overall relative error between the most unfavorable wind pressure coefficient obtained by LBM–LES and the TJ-2 wind tunnel test is less than 15%. The phenomenon of separation and reattachment near the building becomes more complicated as the wind direction angle changes can be captured by LBM–LES.

(2)

The mean base bending moment simulated under different wind direction angles has a small error with the TJ-2 wind tunnel test results. The X-direction bending moment coefficient is generally larger, and the Y-direction bending moment coefficient has a smaller error with the TJ-2 results. This can prove the validity and reliability of the time-averaged results of LBM–LES calculation of building wind load. The root mean square bending moment coefficient obtained by LBM–LES is generally larger than wind tunnel test, which is affected by the inflow turbulence generation.

(3)

The time required for the two-way FSI simulation to record the response of the structure for two cases took over 406 h. The one-way FSI simulation only took 40 clock hours to deduce the response of the structure for two cases. In comparison, the one-way FSI simulation method takes roughly 10% of the clock time required for two-way FSI simulation and, thus, is more feasible for building engineering application.

(4)

The one-way and two-way Fluid–Structure Interaction (FSI) methods based on the Lattice Boltzmann Method (LBM) in this study demonstrate reasonable reproduction of the along-wind mean displacement at the top of the CAARC main building, in comparison with published wind tunnel tests. At a reduced wind speed of 1.5, the crosswind displacements obtained from both one-way and two-way FSI simulations are in close agreement with the results of the wind tunnel tests. However, at a reduced wind speed of 4.6, the vortex shedding frequency approaches the structural natural frequency, leading to a two-fold increase in the crosswind displacement obtained from the two-way FSI simulation compared to that from the one-way FSI simulation. These findings indicate that the LBM method utilized in this study can reasonably simulate vortex-induced vibrations of the CAARC building, providing a new technical reference for vortex-induced resonance in high-rise building structures under strong wind conditions.