To carry out the windresistance performance analysis, the wind load on the building surface must be determined first. The wind load is related to the basic wind pressure, terrain, ground roughness, and building height and shape. In the Chinese Load Code for the Design of Building Structures (the load code) [16], the wind pressure coefficient is introduced to describe the ratio of the actual pressure on the building to the wind pressure calculated from the wind speed. In the load code, only wind pressure coefficients of simpleshaped buildings are provided, whereas traditional buildings with relatively complicated shapes are not included. In this section, the wind pressure coefficients of the main hall of the Tianning Temple are obtained by CFD simulation with Fluent version 16.0. Before starting the simulation of the main hall, preliminary verification work is performed to determine the turbulence model suitable for the case.
Verification of the turbulence model
The large eddy simulation (LES) model and Reynoldsaveraged Navier–Stokes (RANS) kε model are the two main methodologies in practice for evaluating wind effects on buildings. The RANS method relies on a statistical description of the flow, and the kε model provides timeaveraged information of a high Reynolds number and fully turbulent flow with a relatively low computer demand. Theoretically, LES could provide a more accurate simulation relying on transient calculation and enable users to obtain the fluctuating wind loads for structural resistance design and peak wind pressure coefficients for cladding design, but LES requires an increased computational cost by a factor of more than 80 [17]. Out of consideration for the computational cost, the RANS model is a better choice if users care more about the fully developed steady flow rather than the transient changes. Thus, the mean wind pressure coefficients could be assessed using the steadystate RANS model at the significantly reduced cost of computational resources.
Today, in practical applications, the RANS model has been widely used to evaluate the mean wind pressure distribution on a building. The simulation results of the RANS model have been found to be in good agreement with the wind tunnel tests [17,18,19,20,21]. Here, three RANS models (the shear stress transfer (SST) kε model, the renormalization group (RNG) kε model, and the standard kε model) are used to simulate the wind field of a doublepitch roof lowrise building. The simulated wind pressure coefficients are compared with the values suggested by the load code to verify the feasibility of the simulation method and to determine which model is more suitable for the simulation of the main hall.
Verification: computational domain and boundary conditions
The building models are created with the same shape dimensions and roof pitch as the main hall. The computational domain dimensions are selected according to the best practice guidelines of the wind CFD simulation proposed by Franke et al. [22] and Tominaga et al. [23]. The upstream length must be larger than five times the building height and onethird of the whole wind domain length. The blockage rate must be less than 3% to guarantee that the wind around the building can fully develop. The resulting domain dimensions are chosen as 240 m × 140 m × 100 m, which can meet all the above requirements. The building model is placed 80 m away from the wind inlet surface.
The wind domain is divided into three parts (Fig. 5) to simultaneously use the structured and unstructured mesh (Fig. 6). The unstructured mesh (tetrahedral and prism elements) is adopted in the middle part where the building is located because the unstructured mesh adapts better to the irregular shape. Two side parts are built up with the structured mesh (hexahedral elements). There are 489,351 nodes, 99,254 shell elements, and 1,484,365 volume elements in the wind domain.
The inlet boundary was set as the velocityinlet condition, which was imported through the userdefined function (UDF) interface. The inlet boundary is described by the wind velocity, the turbulent kinetic energy k and the turbulence dissipation rate ε. The load code gives the wind velocity expression as follows:
$$u\left(z\right)={u}_{0}{\left(\frac{z}{{z}_{0}}\right)}^{\alpha },$$
(1)
$${k}_{z}=1.5*{\left(u\left(z\right)\cdot I\right)}^{2},$$
(2)
$${I}_{z}=0.1{(z/5)}^{\alpha 0.05},$$
(3)
$${\varepsilon }_{z}={0.09}^{0.75}\frac{{{k}_{z}}^{1.5}}{{l}_{z}},$$
(4)
$${l}_{z}=100{\left(z/30\right)}^{0.5},$$
(5)
where \(z\) is the node height; \({z}_{0}\) = 10 m is the reference height; \(u(z)\) is the wind velocity at the height of z; \({u}_{0}\) is the wind velocity at the reference height; \(\alpha\) = 0.16 is the roughness index; \({I}_{z}\) is the turbulence intensity; and \({l}_{z}\) is the turbulence integral scale. The wind velocity profile at the inlet boundary is shown below in Fig. 7.
The outlet boundary was set as the fully developed outflow condition with zero static pressure. Standard wall conditions were applied for the building surfaces and ground surface. The two overlapping surfaces are set as the interface.
Verification: results
The results show that the RNG kε model performed best among the three models. The wind pressure coefficient contours obtained by simulation using the RNG kε model are shown in Fig. 8, and the comparison with the load code values is illustrated in Fig. 9 (black numbers are simulation results, red numbers are error rate). Therefore, the RNG kε model is considered the best choice in simulating the main hall.
Setup of CFD simulation of the main hall
In the main hall of the Tianning Temple, there are clapboards between the bucket arches (Fig. 3), so the building is in an enclosed state when the doors and windows are closed. In the simulation, the state of open windows and open doors is not considered in this study. The fullscale 3D model of the main hall has been established (Fig. 10).
Two orthogonal wind directions (θ = 0° and θ = 90°) were simulated. θ = 0° is the wind direction perpendicular to the building width, and θ = 90° is the wind direction perpendicular to the building depth. For both wind directions, the wind domain dimensions, boundary conditions and meshing method remain the same as those in the verification case. The final meshed wind domain contains 513,001 nodes, 102,756 shell elements, and 1,688,562 volume elements under θ = 0° and 497,161 nodes, 98,682 shell elements, and 1,490,839 volume elements under θ = 90°. The mesh results (θ = 0°) are shown in Fig. 11.
CFD simulation: results and discussion
Wind flow streamlines
Through the CFD simulation, the wind velocity streamlines around the main hall under the two wind directions were obtained, as shown in Fig. 12.
Wind pressure coefficient distribution
The wind pressure coefficient \({C}_{pi}\) at point i is calculated as:
$${C}_{pi}=\frac{{P}_{i}{P}_{0}}{0.5\rho {{u}_{0}}^{2}},$$
(6)
where \({P}_{i}\) is the wind pressure at point i of the building surface; \({P}_{0}\) is the reference static pressure (air pressure at a height of 10 m)\(;\mathrm{ and} \rho =1.225\mathrm{ kg}/\mathrm{m}\)^{3}, which is the air density.
To better present the results of the wind pressure coefficient distribution, all parts of the building surface are named as follows: the four roofs are named R1 ~ R4, the four eaves are named E1 ~ E4, the eight eave corners are named C1 ~ C8, and the four walls are named W1 ~ W4. The naming result is illustrated in Fig. 13.
The results of the wind pressure coefficient contours of all parts on the building surface under wind directions θ = 0° and θ = 90° can be obtained, as shown in Figs. 14 and 15, respectively.
According to the analysis of Figs. 14 and 15, the following conclusions can be drawn:

(1)
Under the two wind directions, the wind pressure coefficients are distributed symmetrically, and positive wind pressure occurs at the windward surfaces. The closer the area is to the edge, the denser the contour lines are, indicating that the change gradient of the wind pressure is larger in the area near the edges.

(2)
Under the two wind directions, the wind pressures on the crosswind and leeward surfaces are basically negative, and the absolute values of the negative pressure coefficients are all smaller than 1.

(3)
Under the two wind directions, the maximum negative wind pressure occurs at the eave corners, and the coefficient is larger than 2, which means that the eave corners bear a very large wind suction. This large wind suction is also an important explanation for why the corner beams of early Chinese hallstyle timber buildings are designed to be very strong.

(4)
The maximum positive wind pressure coefficient occurs at the central area of the windward pediment when θ = 90°. The coefficients are generally larger than 1. These values also explain why, in most important gableandhip roof timber buildings built since the Song Dynasty, there is always a timber wind deflector set in front of the pediment for buffering the intense wind impact.
The average wind pressure coefficients
The average wind pressure coefficient \({C}_{p}\) of each part of the building surface is computed as:
$${C}_{p}=\sum \left[\frac{{C}_{pi}{A}_{i}}{A}\right],$$
(7)
where \({A}_{i}\) is the surface area of point i, and \(A\) is the overall area of the part where point i is located. The average wind pressure coefficients under the two wind directions are calculated. The results are illustrated in Fig. 16.