# Numerical Analysis of Flow in Building Arrangement: Computational Domain Discretization
## 2 Methods
### Numerical Analysis  
#### 2.3.1 Pre-Processing  
The computational domain represents the research object depicted in Figure 3 placed in a virtual wind tunnel domain of dimensions matching the experimental test section (Figure 4) of the wind tunnel. Moreover, the dimensions correspond with the best practise guidelines by [15]. The meshing was carried out using ICEM CFD 19.2 software. Three different mesh types were used (Figure 5): HEX, POLY and TETRA. For each mesh type, three meshes of different resolutions were generated in order to estimate the discretization error using the GCI method. The relative cell size was defined as the ratio of the average cell size (h) defined with Formula (1) and the base side length of the modelled building (D). Initially, HEX, POLY and TETRA meshes of the relative cell size h/D equal 0.32 were generated.  
Figure 4: Sketch of the experimental test stand.  
where:  
\(\Delta V_{i}\)--the volume of the \(i\)th cell,  
\(N\)--total number of cells in the computational domain.  
The HEX mesh of h/D = 0.32 was prepared using the blocking technique in order to generate perfectly orthogonal cells. The domain was split into 42 blocks and edge parameters (number of nodes and node distribution along a specific edge) were defined for selected edges to control cell sizes distribution. The distribution of nodes along the edges of the modelled buildings was uniform and the node spacing was defined as D/10. The nodes distribution away from the buildings was defined with a sophisticated approach described with Formula (2) with the first layer height equal to D/10. The defined edge parameters were copied to the parallel edges.  
\[S_{i}=\frac{R-1}{R^{n-1}}\sum_{j=2}^{i}R^{j-2} \tag{2}\]  
where:  
\(S_{i}\)--distance from the node on the wall to node \(i\),  
\(R\)--ratio limited by 0.25 \(<R<\) 4.0,  
\(n\)--total number of nodes along the edge.  
The TETRA mesh was created using a top-down meshing approach (OCTREE algorithm) with prism layers. The mesh was intensively smoothed in order to meet the high mesh quality criteria. The mesh resolution was controlled by the global element seed size equal 2D and maximum element size on surfaces representing the walls of the modelled buildings equal D/10 with growth ratio equal to 1.2. The prism layer, which is state-of-the-art in industry, was applied in order to assure finer normal cell sizes perpendicular to the walls of the buildings and the bottom wall. The prism layer consisted of three individual layers of total height equal to D/5, growth ratio equal to 1.2 and exponential growth law.  
The POLY mesh was obtained by converting the TETRA mesh of decreased relative cell size to POLY in Ansys Fluent 19.2 using the standard and fully automatic method described in the Section 1.2.3. Polyhedral mesh. Such procedure allowed to generate POLY meshes of the relative cell sizes matching the ones for HEX and TETRA meshes--0.32, 0.48, 0.64.  
Subsequently, HEX, TETRA and POLY meshes of the relative cell size increased to h/D = 0.48 and finally to h/D = 0.64 were generated by proportional scaling the node distribution and nodes count of the initial meshes (h/D = 0.32).  
Figure 5: The section of the computational domain discretized with the use of HEX, POLY and TETRA elements.