# Numerical Analysis of Flow in Building Arrangement: Computational Domain Discretization
## 4 Discussion  
The mesh convergence analysis was carried out with the use of the GCI method, which is recommended by the Fluids Engineering Division of the American Society of Mechanical Engineers to estimate the discretization error. Three sets of meshes characterized by different relative cell sizes were generated for each of the analysed mesh type (HEX, POLY, TETRA) in order to define mesh convergence and the GCI. The mesh convergence was achieved for each of the analysed mesh types but the GCI for the HEX mesh was the lowest (0.76%) while it was almost three times more in case of TETRA mesh (2.19%). POLY mesh, with GCI = 1.36%, turned out to be advantageous in comparison to TETRA although the prevalence of HEX mesh is unquestionable. The iterations count to convergence of CFD analysis was lower for POLY in comparison to TETRA by 14% (h/D = 0.64), 17% (h/D = 0.48) and 40% (h/D = 0.32). HEX mesh needed the least iterations to achieve convergence of the model except for the case of the lowest relative cell sizes where POLY mesh was the best of all the mesh types. The above-mentioned characteristics did not translate directly to calculation time as each iteration for POLY mesh lasted longer in comparison to both HEX and TETRA meshes. Therefore the analysis with POLY mesh lasted for the longest time for all relative cell sizes. The calculation time was the lowest in case of HEX mesh for relative cell sizes equal 0.48 and 0.64 and in case of TETRA mesh for relative mesh size equal 0.32. The results concerning the relative horizontal (X) velocity profiles for all mesh types and all relative cell sizes indicate very good conformity with PIV data above y/D = 2.0, that is above the taller building. The most significant discrepancies occur close to the ground (bottom wall) approx. up to y/D = 0.3. The differences can be observed not only between the PIV and CFD but also among CFD results for different mesh types. In case of the coarsest meshes (h/D = 0.64), POLY generated too intensive reversed flow between the buildings (X\({}_{11}\), X\({}_{12}\), X\({}_{13}\)), while HEX mesh results were the most comparable to PIV. One of the reasons for the above-mentioned differences between PIV and CFD can be the roughness of the wind tunnel's bottom wall which was not taken into account in the CFD analysis. The differences between the results for the individual mesh types can be justified by the influence of the mesh type characteristics (i.e., numerical diffusivity) as the thickness of the prism layer was identical in case of POLY and TETRA. POLY mesh seems to be the most comparable to PIV for y/D \(\in\) <0.3, 2.0> in the area between the two buildings (X\({}_{11}\), X\({}_{12}\), X\({}_{13}\)). Results for POLY and HEX are comparable to PIV behind the second building, especially for X\({}_{21}\) and X\({}_{22}\). These meshes over predict the reversed flow for X\({}_{23}\). The results for TETRA mesh behind the second building for y/D < 2.0 and h/D = 0.64 do not correspond with PIV as well as CFD for HEX and POLY. Very similar conclusions can be drawn for relative cell size equal 0.48 but POLY and TETRA results are more comparable to each other than it was for h/D = 0.64. Moreover, results for TETRA behind the second building (especially for X\({}_{21}\) and X\({}_{22}\)) are in better agreement with PIV as well as with CFD for HEX and POLY. The discrepancies between PIV and CFD results in case of the finest meshes (h/D = 0.32) are, in general, similar as for the coarser meshes (h/D = 0.48 and 0.64) but the differences between the mesh types are less intensive. POLY and TETRA results are almost in a perfect match between the buildings while HEX and TETRA results are more consistent after the second building. The in-depth analysis of the relative horizontal (X) velocity field indicates an acceptable qualitative agreement of the PIV and CFD results although quantitative differences are noticeable.