## 3 Methodology
### Simulation of Outdoor Environmental Performance in Urban Blocks
#### 3.4.1 Simulation of Universal Thermal Climate Index (UTCI) at Pedestrian Height  
The Universal Thermal Climate Index (UTCI) is an index used to describe human thermal comfort in outdoor environments [72]. It is based on human physiological research and the thermal radiation balance theory and assesses the human thermal stress response by integrating environmental parameters [74]. The UTCI is one of the most widely used thermal comfort assessment indicators internationally. Therefore, the UTCI is crucial for evaluating the impact of outdoor environments on human health. The calculation formula for UTCI is as follows:  
\[UTCI=f(T_{a};\ MRT;v_{10};RH) \tag{1}\]  
where \(T_{a}\) represents the air temperature, \(MRT\) denotes the mean radiant temperature, \(v_{10}\) indicates the wind speed, and \(RH\) stands for relative humidity [75].  
The numerical simulation of the UTCI for urban blocks involved several key parameters. First, the basic environmental data required for UTCI calculation, such as air temperature and relative humidity, were obtained from the EPW meteorological data of Beijing (weather station ID: 545110). Second, to acquire the wind data needed for UTCI calculation, the wind speed and direction data collected in the first step were imported into the virtual wind tunnel simulation module of the Butterfly plugin to ensure that the simulation process aligned with actual climatic conditions. Specifically, the Butterfly plugin was used as an interface to construct a virtual wind tunnel in BlueCFD, providing the necessary support for wind speed simulation. In this study, based on the actual environmental characteristics of Beijing, the surface roughness length was set to 0.5, and the wind tunnel calculation domain boundary was defined as 5H\({}_{\text{max}}\) (where H\({}_{\text{max}}\) refers to the maximum building height within the block). The wind environment detection plane was set at a pedestrian height of 1.5 m, with 121 monitoring points (11 \(\times\) 11) arranged within the plane. Both the top and side boundaries were configured as symmetric boundary conditions to ensure that the wind speed, direction, and flow characteristics matched the actual environmental conditions.  
Figure 6: UTCI calculation flowchart. The arrows in the figure represent the simulation and calculation process of UTCI values using basic climate data.  
The third step involved calculating the mean radiant temperature (MRT), which represents the actual temperature of an object influenced by radiant heat. The Radiance plugin within Ladybug Tools was utilized to calculate the mean radiant temperature of building surfaces and the surrounding environment. For this study, MRT monitoring points were placed at a height of 1.5 m, with a total of 225 points (15 \(\times\) 15).  
Finally, the average air temperature, MRT, wind speed, and relative humidity data for the selected dates were input into the UTCI module of the Ladybug plugin for calculation. Extreme heat and cold weeks were chosen as the calculation periods to comprehensively evaluate environmental performance under different climatic conditions.