A Generalization of Building Clusters in an Urban Wind Field Simulated by CFD

Abstract

The urban climate has a critical influence on developing sustainable cities, and one important factor is the urban wind environment. Moreover, refining urban wind fields is required for the quantitative assessment of urban wind environments. Computational fluid dynamics (CFD) is a powerful tool for modeling the wind flow characteristics in urban areas. Although CFD has been widely used in various fields, its use for simulating urban wind fields has limitations because of the complexity of urban building models and the high computational workload. Accordingly, we consider the generalization parameters in the vertical and horizontal directions based on the CFD results and the building topology based on the state of the building nodes. We perform a two-dimensional generalization of building clusters, conduct spatial analysis in a geographic information system (GIS), and generate three-dimensional models. This generalization scheme is applied to Meiling Street in Jinjiang City, Fujian Province, China. The results indicate that the generalization decreases the number of buildings from 7003 to 3367 and the computation time from 11 h and 26 min to 10 h and 25 min. The computation efficiency is improved by 8.89%, with 1.85% changes in the average wind speed ratio. This scheme substantially improves the computational efficiency of urban wind field CFD simulations by reducing the geometric model’s complexity without compromising the accuracy. This strategy is suitable for simulating large-scale urban wind fields.

1. Introduction

Cities worldwide and building densities have grown significantly [1]. It is estimated that 68% of the global population will reside in urban areas by 2025. Environmental issues related to the wind environment caused by urbanization have impacted urban air quality, residential comfort, and building energy consumption [2,3,4,5]. Therefore, high-resolution simulations of urban wind environments are required, as well as monitoring, planning, designing, and risk assessment of urban wind environments [6]. Early research on wind environments focused on wind tunnel experiments and field measurements. However, both methods are time-consuming and costly [7,8]. With the development of computer technology, computational fluid dynamics (CFD) has been increasingly used for climatic modeling of urban areas [9,10,11]. CFD has a relatively low cost and time consumption and can accurately model three-dimensional velocity, temperature and pressure fields, and other variables inside and outside buildings. Accordingly, CFD has been used extensively to evaluate the outdoor wind environment of buildings to guide architectural design and planning [12,13]. Hnaien developed a city model with building details for the Hail region and conducted CFD simulations to identify areas with low wind comfort. The results showed that the weather conditions (wind speed and direction) and building layout significantly affected comfort [14]. Vita combined CFD and dynamic thermal modeling (DTM) to assess the airborne infection risk in buildings and make buildings safer during an epidemic [15]. Hågbo selected five urban areas with different forms to assess pedestrian wind comfort and safety for multiple wind directions. The results revealed the interaction between the urban form and wind direction and provided an important reference for urban planning and design [16].

Building clusters are the primary factor affecting wind fields in urban areas. The geometric shape, layout, height, and orientation of buildings influence the wind flow field [17,18,19]. However, it is difficult and time-consuming to consider the detailed characteristics of individual buildings to describe the wind field of the urban environment accurately. A complex model of many buildings significantly increases the number of grids in the CFD simulation and the computational complexity of modeling, decreasing simulation efficiency [20,21].

Therefore, it is necessary to simplify the building clusters for modeling the influence of buildings to reduce the time and cost of CFD simulations of the urban wind environment. Ricci [22] assessed the numerical simulation discrepancies resulting from geometric simplification. They conducted wind tunnel tests and CFD simulations with three simplification levels in the Quartiere La Venezia area. The results indicated that the CFD simulations with detailed geometric models were closest to the wind tunnel results. However, the study area was relatively small. Thus, the computational efficiency was not improved significantly. Guo [23] expanded their study area to an entire campus building, and in order to improve the computational efficiency, they simplified the buildings by adjusting different parameters. However, this scheme is only suitable for cuboid buildings, and the effect is not good for more complex and large buildings. In order to enable CFD to be applied to a wider range of research areas, Li [24] used a geographic information system (GIS) to merge and generalize the building clusters in two dimensions and performed a CFD wind environment simulation for Jinjiang City. Subsequently, they generated three-dimensional models from the simplified representations. The results showed a significant improvement in CFD computational efficiency after the generalization, with a good correlation between the simulated and measured wind speeds. Back presented a 2.5D method integrating CFD and a GIS for fine-scale studies of urban environments. This approach enabled more comprehensive evaluations of urban heat islands and human thermal comfort, contributing to the sustainable development of resilient cities [6]. GISs have a unique advantage for researching urban building cluster wind environments. The spatial analysis functions efficiently process two-dimensional graphics, attribute analysis provides valuable floor-level statistics, graphic aggregation enables merging structures, and polygon simplification streamlines topological complexities [25,26,27].

Scholars conducted extensive research on urban building group modeling to perform CFD simulations of urban wind fields. However, these modeling methods have limitations. For example, no systems exist for parameter selection, and the influence of the generalization on CFD simulations of wind environments has not been determined. As a result, large differences exist between the original and merged building groups, affecting the accuracy of wind environment simulations. Therefore, it is necessary to develop a suitable generalization scheme for CFD simulation of large-scale urban building groups to improve the efficiency and accuracy of CFD simulations of urban wind fields.

We chose Meiling Street in Jinjiang City as the study area, and we propose a new building cluster generalization scheme. We utilize results from various CFD simulations to establish building generalization parameters in a GIS. The parameters include the height, distance, and topological characteristics of buildings. This scheme ensures that parameters affected by the wind conditions are selected, enhancing the method’s suitability for building generalization in CFD wind environment simulations. Generalizing parts of the building reduces model complexity while retaining the wind field conditions, balancing the calculation efficiency and accuracy. This strategy has substantial potential for CFD simulations of urban wind fields.

2. Materials and Methods

2.1. Study Area

This study used Meiling Street in Jinjiang City, Fujian, China as the study area (Figure 1). The street is located in the northern part of Jinjiang City. It covers approximately 10 square kilometers and runs through the central urban area. The area has a high building density with many commercial and residential centers, seamlessly integrating traditional single-story structures with modern multi-story buildings.

The building outline data were provided by the Jinjiang City government, and the meteorological data were sourced from the Jinjiang Meteorological Bureau. The 30 year (1991–2021) wind direction and wind speed data were obtained from the Jinjiang Meteorological Station on Meiling Street. The Jinjiang Meteorological Station, located at 24.82° N and 118.57° E, is a national reference station. Statistical analysis of the wind direction and wind speed revealed that the predominant wind direction was from the northeast, with a multi-year average wind speed of 3.96 m/s. This study assumed typical annual climatic conditions under the influence of the dominant wind.

2.2. Generalization Scheme

Generalization in this study refers to merging buildings with similar distances and heights into a building group with a unified height using three generalization parameters (the height difference between buildings, distance between buildings, and tolerance of topological simplification of the buildings). The topology of the merged buildings was simplified, and the complexity of the generalized building group model was reduced. The building vector layer in the ESRI shapefile (shp) format contained spatial and attribute information on the buildings. The two-dimensional building clusters were generalized using GIS analysis. Subsequently, a three-dimensional building cluster model was generated. The objective was to reduce the number of buildings and model complexity while preserving the wind flow field. The generalization workflow is depicted in Figure 2. (1) To avoid inappropriate merging of buildings on opposite sides of the roads, we initially divided the study area into multiple zones (e.g., shp_1, shp_2, shp_3... shp_i) based on the administrative boundaries and major roads in the study area. (2) One of the zones, shp_i, was selected for the generalization. (3) The floors were ranked to ensure uniformity for the building heights. The frequencies of the number of floors in buildings in shp_i were ranked in descending order. All buildings that met the vertical generalization parameters were selected based on the floor height. For instance, if the most common floor height in the zone was 3 m, and the vertical generalization parameter was 3 m, then all buildings with heights ranging from 3 m to 6 m were selected for generalization. (4) The selected buildings satisfying the horizontal generalization parameters were consolidated and merged into a new building with the assigned basic floor height. In this example, the horizontal generalization parameter was 5 m. Thus, all buildings within a distance of less than 5 m were merged. (5) The bend simplification algorithm was chosen to simplify the results from step 4. This algorithm defines the maximum angle that can be considered a straight line in a polygon based on a bend threshold. If the angle between each pair of adjacent line segments is below the threshold, then they are joined to form a new curve approximating the original line segment [28]. This algorithm produces fewer sharp angles than other polygon simplification algorithms. This step eliminates small curvatures at the building boundaries, preserves polygon shapes, reduces the vertex count, and decreases computational complexity and storage space. In this example, we used a topological tolerance of 10 m, and the simplified results were applied to the aggregated buildings after step 4, completing the generalization of floor_i. (6) The generalization was performed for each floor in each zone. The results from step 5 were replaced with the original zone’s building representation, serving as the new baseline layer. Steps 3–6 were repeated in the next floor generalization. For instance, if the next height of floor_2 was 9 m, then all buildings with heights from 6 m to 12 m were selected. This process continued until all floors were generalized. The same steps were applied to the next zone. (7) The last step involved consolidating the results obtained from the zone-by-zone generalization to achieve a generalization representation of the study area.

2.3. CFD Simulation

The average wind speed derived from statistical analysis (3.96 m/s) was utilized as the reference wind speed at the standard height (10 m) in the CFD simulations. The dominant northeast wind direction and the east and north wind directions were considered when selecting the horizontal and vertical generalization parameters. However, only the northeast wind direction was used when the generalization scheme was applied to the entirety of Meiling Street in the CFD simulations.

Choosing a rather small computational domain may reduce computational precision, whereas an excessively large domain can lead to an excessive number of grid cells, increasing the computational load. Therefore, we used the standards established by the AIJ research institution [29] to select the distances from the top and side boundaries of the computational domain to the building boundaries. The minimum distance was 5H (maximum building height), and the minimum distance from the outflow boundaries to the building boundaries was 10 H. In our study, the maximum building height was 96 m, and the distances from the top and side boundaries were 600 m and 2200 m, respectively, meeting the standard, as illustrated in Figure 3.

Due to the complex building distribution, we used unstructured grids for meshing to enhance the adaptability to boundary flow fields with complex shapes and facilitate the refinement of areas with large changes in building geometry. We selected three grid sizes to test the grid sensitivity (

Table 1. The maximum mesh size for different parts.

	Global	Ground	Buildings	Total Grid Numbers
Case 1	100 m	40 m	6 m	671,477
Case 2	80 m	20 m	6 m	2,009,687
Case 3	60 m	8 m	4 m	4,888,991

). Due to the large size of the study area and limited computational resources, we chose to test a small area rather than the entire study area. A total of 45 reference points were selected to compare wind speeds at a 1.5 m height for different cases, as shown in Figure 4. The wind speeds of the reference points for Case 2 and Case 3 were only slightly different. The wind speed correlation between Case 1 and Case 2 was 0.48, and that between Case 2 and Case 3 was 0.94. Since we analyzed the wind environment of the entire street, Case 2 and Case 3 were applicable to the study area. However, the number of grids for the entire city was too large when the grid size was the same as that in Case 3 and exceeded the computer limit. Therefore, the maximum grid size was set to 80 m for the global element, 20 m for the ground, and 6 m for the buildings. Although most meshes were in the recommended range of 30–10,000 for y+ [30], some meshes deviated from this range due to limited computer resources and complex computational domain surfaces. Since y+ is often not defined in practice, the grids were not redivided in this study. Figure 5 is a schematic diagram of the grid used in the study area.

ANSYS FLUENT was used as CFD numerical simulation software. We used the finite volume method to solve the numerical problem and ensure that the physical laws of the volume elements were satisfied. The finite volume method has been widely used for flow field analysis and fluid calculations and is the prevalent numerical solution method in fluid mechanics. The standard k-ε model was used as the turbulence model [31], and the averaged Navier–Stokes equations are as follows:

$$\begin{array}{c}\frac{\partial u_i}{\partial x_i}=0\end{array}$$

(1)

$$\begin{array}{c}{U}_j\frac{\partial U_i}{\partial x_j}=-\frac{1}{\rho }\frac{\partial P}{\partial x_i}+\frac{\partial }{\partial x_j}\left(\mu \frac{\partial U_i}{\partial x_j}\right)+\frac{\partial }{\partial x_j}\left(-\overline{u_i{u}_j}\right)\end{array}$$

(2)

where $U_i$ and $u_i$ are the mean and fluctuation parts of the velocity components, respectively, and $x_i$ and $x_j$ are the coordinate directions. $P$ is the mean static pressure, and $\rho$ is the fluid density. In the standard k-ε model, the relationship between the Reynolds stress term and the mean velocity component is as follows:

$$\begin{array}{c}-\overline{u_i{u}_j}=2C_{\mu }k{s}_{ij}-\frac{2}{3}k{\delta }_{ij}\end{array}$$

(3)

where $C_{\mu }$ is the empirical constant, $k$ is the turbulent kinetic energy, and ${\delta }_{ij}$ is the Kronecker delta. Therefore, the governing equations of turbulent kinetic energy $k$ and turbulent dissipation rate ε are as follows:

$$\begin{array}{c}{U}_j\frac{\partial k}{\partial x_j}=\frac{\partial }{\partial x_i}\left[\left(\mu +C_k\frac{k^2}{\epsilon }\right)\frac{\partial k}{\partial x_j}\right]-\overline{u_i{u}_j}\frac{\partial U_i}{\partial x_j}-\epsilon \end{array}$$

(4)

$$\begin{array}{c}{U}_j\frac{\partial \epsilon }{\partial x_j}=\frac{\partial }{\partial x_j}\left[\left(\mu +C_{\epsilon }\frac{k^2}{\epsilon }\right)\frac{\partial \epsilon }{\partial x_j}\right]-C_{\epsilon 1}\frac{\epsilon }{k}\overline{u_i{u}_j}\frac{\partial U_i}{\partial x_j}-C_{\epsilon 2}\frac{{\epsilon }^2}{k}\end{array}$$

(5)

where $\mu$ is the viscosity of fluid and the constants $C_{\mu }$, $C_k$, $C_{\epsilon }$, $C_{\epsilon 1}$, and $C_{\epsilon 2}$ take the values 0.09, 0.09, 0.07, 1.44, and 1.92 respectively.

Numerous engineering application practices have shown that this model can calculate relatively complex turbulence with high stability and accuracy [32,33]. Meanwhile, the SIMPLEC algorithm was used to accelerate the convergence because it uses a small relaxation coefficient. Convergence occurred when all scaled residuals leveled off. The outlet conditions were zero static pressure. The top of the domain was modeled as a symmetrical surface or as a mirror. The wall functions were used for the ground and the building surfaces. A velocity boundary condition was applied at the inlet. The inlet velocity was defined using the exponential wind profile model:

$$U_Z=U_r{(\frac{Z}{Z_r})}^{\alpha }$$

(6)

where $U_Z$ is the average wind speed at a certain height, $Z$ is the height corresponding to the average wind speed $U_Z$, $U_r$ is the wind speed at the reference height, $Z_r$ is the reference height (we used the observation height of the weather station (10 m)), and α is the coefficient of the terrain classification. Since the class was a city with dense building groups and large building heights, 0.3 was used for $\alpha$ according to the building load specification [34].

3. Results

3.1. Generalization Parameters

The morphological characteristics of the building were the dominant factor affecting the complexity of the building group. The CFD simulation required substantial computing resources due to the complexity and diversity of the building forms. The buildings were generalized vertically, horizontally, and topologically. A key issue in generalizing building clusters is selecting the generalization parameters. If the generalization parameter threshold is too large, then many building features are eliminated. If the generalization parameter threshold is too small, then the generalization effect is insufficient, reducing the computational efficiency. Therefore, it is necessary to conduct parameter selection experiments to clarify the three parameters and select an appropriate generalization parameter scheme for the study area.

The parameters in the vertical and horizontal directions of the building were selected based on the changes in the CFD simulation of the wind environment before and after generalization. The dominant wind direction from the northeast and two adjacent wind directions (north and east) were used in the simulation. The wind speeds were based on the multi-year average of the study area (3.96 m/s). Vertical generalization aims to standardize buildings with height differences within a certain range to the same height. Horizontal generalization aims to merge buildings within a specific distance to reduce the number of buildings. The selection of the building topology generalization parameters depends on the state of the building nodes before and after generalization. Following horizontal and vertical generalization, small buildings may be merged into new buildings. Topological generalization aims to reduce the redundant nodes of the new buildings while maintaining the morphological characteristics. Figure 6 shows the schematic diagram of the buildings in two and three dimensions before and after the generalization of a zone.

3.1.1. Vertical Generalization Parameters

Since 62.35% of the building area fell within 150 m² ± 50 m², 98.64% of the building floors were 30 m and below. Therefore, we used a model length of 15 m and a width of 10 m for the generalization parameter selection in the vertical direction. We assessed 10 building heights (3–30 m at intervals of 3 m) to select the vertical generalization parameters.

CFD wind environment simulations were performed for different building heights. The wind speed ratios at the pedestrian height (1.5 m) for three incoming winds (northeast, north, and east) are depicted in Figure 7. In general, the wind speed ratio increased as the building height increased, and the rate of increase was larger for taller buildings. The main reason for this is that the wind speed on both sides of the building increases with the building height. In addition, the spatial distribution of the wind speed ratio around the buildings is more similar for taller buildings. For example, the wind speed ratio exhibited greater consistency at building heights of 3 m and 6 m. However, there were notable differences in the wind speed ratio between the 30 m buildings and shorter buildings.

Table 2. Average wind speed ratio at different building heights for each wind direction.

Height	3 m	6 m	9 m	12 m	15 m	18 m	21 m	24 m	27 m	30 m
NE	0.9673	0.9457	0.9773	1.0155	1.0045	1.0221	1.0643	1.0822	1.1232	1.1615
N	0.9409	0.9394	0.9678	1.0147	1.0193	1.0671	1.1197	1.1762	1.2555	1.3109
E	0.9997	0.9717	0.9708	0.9876	0.9662	0.9942	1.0251	1.0579	1.1105	1.1452

shows the average wind speed ratio in the computational domain, which exhibits an upward trend for the three wind directions as the building height increased. The rate of increase in the average wind speed ratio was larger when the incoming wind direction was north. As the building height increased from 3 m to 30 m, the average wind speed ratio increased from 0.9673 to 1.1615 for the northeast wind, from 0.9409 to 1.3109 for the north wind, and from 0.9997 to 1.1452 for the east wind. Therefore, the largest increase in the wind speed ratio occurred when the incoming wind direction was perpendicular to the building direction, followed by the incoming wind direction at an angle of 45°, with the building direction and the incoming wind direction parallel to the building direction.

Table 3. Differences in average wind speed ratios at different height differences in each wind direction.

	NE	N	E	Total
$∆$h3	0.0215	0.0411	0.0161	0.0252
∆h6	0.0464	0.0857	0.0353	0.0539
∆h9	0.0681	0.1277	0.0530	0.0797

lists the differences ($∆h$) in the wind speed ratios before and after building generalization for three building heights (3 m, 6 m, and 9 m) and different wind directions. Equation (7) was used for this calculation:

$$∆h_i=\frac{\sum |∆U_i|}{j}$$

(7)

where i denotes the building height (3, 6, and 9 m), and j denotes the number of $∆U_i$ (9, 8, and 7). A weighted average of the three wind directions was calculated according to the proportion of the wind directions obtained from the meteorological station:

$$∆{total}_{(\mathrm{3,6},9)}=a\ast ∆{NE}_{\left(\mathrm{3,6},9\right)}+b\ast ∆N_{\left(\mathrm{3,6},9\right)}+c\ast ∆E_{\left(\mathrm{3,6},9\right)}$$

(8)

where $a$, $b$, and $c$ are the frequencies of the wind speed from each wind direction in the study area. Due to the model symmetry, the CFD simulation results were the same for the north and south, east and west, northeast and southeast, and northwest and southwest wind directions. Thus, the results for the same wind directions were combined, and therefore $a$ was 0.5083, $b$ was 0.255, and $c$ was 0.2367. Equation (8) was transformed as follows:

$$∆{total}_{(\mathrm{3,6},9)}=0.5083\ast ∆{NE}_{\left(\mathrm{3,6},9\right)}+0.255\ast ∆N_{\left(\mathrm{3,6},9\right)}+0.2367\ast ∆E_{\left(\mathrm{3,6},9\right)}$$

(9)

The average wind speed ratio difference was 0.0252 for a building height difference of 3 m, 0.0539 for a building height difference of 6 m, and 0.0797 for a building height difference of 9 m. The difference in the wind speed ratio was the largest when the incoming wind direction was north (i.e., perpendicular to the building’s direction), followed by the wind direction at a 45° angle to the building’s direction and the incoming wind direction parallel to the building’s direction.

In summary, the larger the height difference between the buildings, the greater the impact on the wind speed ratio. Therefore, it is advisable to keep the values of the generalization parameters small to minimize the impact of the wind environment. Moreover, since the purpose of vertical generalization is to merge scattered shanty towns and non-standard low-rise buildings renovated by residents, most of the height differences were within 3 m. Therefore, 3 m was selected as the vertical generalization parameter.

3.1.2. Horizontal Generalization Parameters

Two identical cuboids with a building length of 15 m, a width of 10 m, and a height of 15 m were selected as the basic building to select the horizontal generalization parameters. The standard width of sidewalks in urban areas is 1.5–2.5 m, and the lane width is 3.5–3.75 m or wider. A distance of 7.5 m corresponds to the width of double lanes. Using a larger distance may have resulted in the inappropriate merging of buildings. Therefore, we selected 2.5 m, 5 m, and 7.5 m as the distances to conduct generalization parameter tests in the horizontal direction and select the optimum generalization parameters for assessing the wind environment.

The wind speed ratios at the pedestrian height (1.5 m) for three incoming wind directions (northeast, north, and east) are shown in Figure 8. The wind speed ratio around the building was the smallest when the incoming wind direction was east. The wind speed ratio exhibited a negligible change after generalization. It was low at the back of the building and relatively high on both sides. The wind speed ratio in the high-value area on both sides of the building was higher for the northeast or north wind directions. This occurred because the wind velocity is higher in the gap between two buildings. The windward area of the building was higher after the generalization, and the wind flowed around the sides of the merged building instead of between them.

Table 4. Difference in average wind speed ratio between different building distances.

Distance	NE1	NE2	∆NE	N1	N2	∆N	E1	E2	∆E	∆Total
2.5 m	1.1900	1.2042	0.0142	1.2232	1.2295	0.0063	1.1924	1.2018	0.0094	0.0111
5 m	1.1815	1.2041	0.0226	1.2197	1.2267	0.0070	1.1895	1.1975	0.0079	0.0152
7.5 m	1.1809	1.2055	0.0245	1.2179	1.2272	0.0093	1.1889	1.1975	0.0086	0.0168

lists the differences in the wind speed ratio for different wind directions before and after the horizontal generalization. The average wind speed ratio was higher after generalization for the three wind directions due to an increase in the wind speed ratio in the bypass area. The average wind speed ratio was higher for the northeast direction than for the northeast and north winds. The difference in the average wind speed ratio was also the largest for the northeast direction. Therefore, it can be inferred that the northeast wind has the greatest influence on the horizontal generalization of buildings. When the incoming wind direction was northeast and north, the average wind speed ratio increased with the building’s distance. The average wind speed ratio changed slowly as the distance increased from 2.5 m to 5 m for the northeast wind. When the incoming wind direction was east, the average wind speed ratio initially decreased and then increased with the distance between buildings, and the difference was the smallest for a distance of 5 m. In summary, no correlation existed between the changes in the average wind speed ratio and the distance between buildings. The weighted average wind speed ratio increased from 0.0111 to 0.0168 as the distance increased from 5 m to 7.5 m. Therefore, a building distance of 5 m was selected for the horizontal generalization parameter.

3.1.3. Topological Generalization Parameters

Topological generalization is performed after vertical and horizontal generalizations because multiple buildings have been aggregated into a new building. Topological generalization is performed to reduce the redundant nodes of the new buildings. Here, buildings with more than 20 sides were regarded as objects that required topological generalization. Ten sides were used as intervals for classification (those with more than 100 sides were unified into one category), and a building was extracted. We extracted one polygon from each category and performed topological generalization with a range of 1–15. Figure 9 shows that the number of nodes decreased as the generalization parameter increased. We used dynamic programming to analyze the breakpoints and observe six instances at a topological parameter of 6 m. This result indicates that the change in the number of building nodes was negligible after reaching a topological tolerance of six. Therefore, 6 m was chosen as the parameter value for the topological generalization.

In summary, we used 5 m for the horizontal generalization parameter, 3 m for the vertical generalization parameter, and 6 m for the topological generalization parameter. Figure 10 illustrates the results of applying the generalization scheme to the building clusters in the entire study area. Two regions with significant changes after the generalization are enlarged for closer inspection.

3.2. Generalization Scheme Verification

3.2.1. Generalization Efficiency

The generalization flow in Section 2.2 was used to generalize the Meiling Street buildings and conduct CFD simulations.

Table 5. Comparison of indicators before and after generalization of Meiling Street.

	Number of Buildings	Model Data Size	Number of Grids	Number of Nodes	Calculation Time
Before	7003	272 MB	30,190,746	5,359,711	11 h 26 min
After	3356	199 MB	29,898,895	5,299,814	10 h 25 min

lists the generalization results for Meiling Street, including the number of buildings, the model size, the number of grids for the same grid settings, the number of nodes, and the calculation time. The number of buildings, the model size, the number of grids, and the number of nodes were substantially lower after generalization, indicating a significantly lower complexity for the generalized geometric model. The CFD calculation efficiency was significantly lower after generalization. A computer with an Intel(R) Core (TM) i9-1090OK CPU @ 3.70 GHz was used. In this case, the CFD solution time was reduced from 11 h 26 min to 10 h 25 min, and the efficiency increased by 8.89%.

3.2.2. Comparison of the Wind Environment

The wind speed contours before and after generalization of Meiling Street were compared. Figure 11 illustrates the wind speed ratio before and after the generalization of the study area at the pedestrian height (1.5 m). The wind speed ratio behind the building clusters was low, and the ratio on both sides was high before and after generalization. The average wind speed ratio was 0.54 before generalization and 0.55 after generalization, an increase of 1.85%, which indicates a minimal difference.

Figure 12 compares the spatial distribution of the wind speed ratio at the pedestrian height (1.5 m) before and after the generalization of four buildings with typical layouts (enclosed building layout, building layout parallel to the incoming wind direction, building layout perpendicular to the incoming wind direction, and mixed building layout). Case A represents the distribution of the wind speed ratio before generalization, Case B represents it after generalization, and Case C represents the difference in the wind speed ratio between Case A and Case B. The average wind speed of the building groups in the four layouts was slightly higher after generalization. The average wind speed ratio of the enclosed layout (Zone A) was 1.31 before generalization and 1.32 after generalization. The largest difference in the wind speed ratio occurred between the interior of the building clusters and the original building. The wind speed inside the building group was relatively stable after generalization, and the wind shadow area was smaller than it was before generalization. The average wind speed ratio of Zone B, a building group parallel to the incoming wind direction, was 1.23 before generalization and 1.24 after generalization. The wind shadow area between the buildings was significantly lower, and the wind speed ratio was slightly higher after generalization. Zone C, a building group perpendicular to the incoming wind direction, had the highest wind speed ratio. The average wind speed ratio was 1.38 before generalization and 1.41 after generalization. The wind shadow area was significantly different after generalization. The wind flowed between the buildings before generalization but was blocked by the building after generalization, substantially changing the shape of the wind shadow area. The average wind speed ratio of the mixed layout (Zone D) was 1.22 before generalization and 1.24 after generalization. In this case, the wind speed ratio of the building cluster was slightly higher after generalization than before generalization. After generalization, the mixed buildings tended to be parallel to the incoming wind direction. Therefore, the tunnel effect was more pronounced after generalization.

We compared the wind speed before and after the generalization of the whole study area and extracted the wind speed at reference points at the same distance for the four layout scenarios at a height of 1.5 m. The results are illustrated in Figure 13. It is noteworthy that the frequencies were normally distributed in all five cases. The maximum difference in the wind speed at the reference points before and after generalization was 1.2 m/s on Meiling Street, and the difference in wind speed within 0.2 m/s accounted for more than half of it. The maximum wind speed difference for the four layouts was 0.6 m/s. The difference in the wind speed before and after generalization was the smallest in Zone A, with 94% being within 0.2 m/s. In contrast, the difference was the largest in Zone B, being only 73% within 0.2 m/s. The proportions were similar for Zones C and D. However, 64% of the reference points in Block C had higher wind speeds after generalization, whereas 58% of the points in Block D had lower wind speeds. The differences in wind speed before and after generalization were within 0.2 m/s for more than half of the reference points in the five cases, indicating a minimal error in the wind speed.

Three evaluation indicators were selected to assess the accuracy of the wind speed after generalization [35]: the fractional bias (FB), normalized mean square error (NMSE), and correlation coefficient (R):

$$FB=2\frac{\overline{U_{CFD2}}-\overline{\overline{U_{CFD1}}}}{\overline{U_{CFD2}}+\overline{U_{CFD1}}}$$

(10)

$$NMSE=\frac{{\left(\overline{U_{CFD2}-U_{CFD1}}\right)}^2}{\overline{U_{CFD2}}·\overline{U_{CFD1}}}$$

(11)

$$R=\frac{\left(\overline{U_{CFD2}-\overline{U_{CFD2}}}\right)-\left(\overline{U_{CFD1}-\overline{U_{CFD1}}}\right)}{{\sigma }_{U_{CFD2}}·{\sigma }_{U_{CFD1}}}$$

(12)

where U_CFD1 and U_CFD2 are the average wind speed (m/s) before and after generalization, respectively, and σ is the standard deviation of the data set. The optimum results were obtained when FB = 0, NMSE = 0, and R = 1.

Table 6. Validation metrics for 5 scenarios.

	FB	NMSE	R
Meiling Street	0.016393443	0.000393496	0.692922113
Zone A	0.007604563	0.000099242	0.816769689
Zone B	0.008097166	0.000099194	0.779068853
Zone C	0.021505376	0.000880851	0.93987057
Zone D	0.016260163	0.000393548	0.843616078

lists the results before and after generalization of Meiling Street for the four layouts (at a 1.5 m pedestrian height). The NMSE of Meiling Street was the lowest, but the values were similar for the five scenarios. The consistency between the FB and R was lower for Meiling Street than for the other four layouts. Therefore, the wind environment differences were larger for Meiling Street than in the other four zones, consistent with the results in Figure 13. The FB was higher in Zones A and B than in Zones C and D, and the R value was smaller in Zones A and B than in Zones C and D. Overall, the wind environment was relatively consistent before and after generalization.

4. Conclusions and Discussion

This paper proposed a generalization scheme for CFD wind environment simulations. A CFD numerical simulation was used to select the generalization parameters, and GIS analysis was conducted to perform vertical, horizontal, and topological generalizations of buildings. A case study of Meiling Street in Jinjiang City was conducted. The following results were obtained:

(1)

The computing speed of the CFD simulation depended on the number of model grids and nodes. The computing speed was improved by generalizing the building clusters. However, the computational efficiency was not the highest for the largest generalization index. The generalization parameters must be selected based on specific conditions. Otherwise, an overgeneralization of the building groups may not accurately represent the wind environment and may produce new nodes that reduce the calculation efficiency.

(2)

We assessed three wind directions to select the CFD generalization parameters. The optimal generalization parameter values were 3 m in the vertical direction, 5 m in the horizontal direction, and 6 m for the building topology. The model was simplified, and the data volume was reduced after generalization. The calculation efficiency was 9% higher, and the accuracy was 2% lower after generalization, indicating that the proposed method is suitable for large-scale CFD simulations of urban wind environments.

(3)

The average wind speed was higher after generalization because the heights and sizes of some buildings were changed by the generalization, and wind shadow areas occurred between some buildings. The wind shadow area was smaller after the buildings were merged in the generalization, and the wind flowed around the sides of the building, resulting in an increased wind speed on both sides.

The computational efficiency improvement of 8.89% means that one hour is saved every 11 h, and the generalization process for the whole study area only requires a few minutes. Therefore, the improvement in computational efficiency is significant. But the proposed generalization scheme has some limitations. We only used three generalization parameters for the building data in the study area. More parameter elements could be included, such as the angle between buildings and the influence of buildings on terrain relief. The measured data could be compared with the simulation results for verification. The generalization of building clusters reduced the computational load but resulted in errors. Therefore, trade-offs and choices must be made according to the research goals and accuracy requirements. It is necessary to select generalization parameters suitable for the study area and building conditions and consider specific research objectives and accuracy requirements. Adiabatic conditions were used in the CFD simulations, and thus atmospheric stability was not considered, which is one limitation of this study. The effect of solar thermal radiation will be evaluated in a follow-up study.