# Development of Building CFD Model Design Process Based on BIM
## 4 Validation through Comparison with Commercial CFD Tool
### Validation Method  
The developed method was validated by analyzing the effects on the grid model and the accuracy of simulation results according to the optimization. First, the effect of the optimization was analyzed by comparing the number of grids and the grid quality of each target CFD model. The total number of grids and grid quality of the optimized CFD model through the proposed method were compared with the CFD model with the original shape applied for the same target. Skewness and non-orthogonality was used for the grid quality parameters, which are commonly used in CFD studies [34]. Figure 4 shows how to estimate skewness and non-orthogonality. Skewness is an index to assess the numerical diffusion error in the process of finite volume discretization. As shown in Equation (3), It is calculated as the ratio of the vector \(\overrightarrow{c}\), which connects the center points (\(P\), \(Q\)) of two adjacent cells, and \(\overrightarrow{d}\), which is the distance between center point (\(M\)) at which two cells intersect and vector \(\overrightarrow{c}\).  
\[\mathbf{\epsilon}=\frac{\left|\overrightarrow{d}\right|}{\left|\overrightarrow{c }\right|} \tag{3}\]  
where, \(\mathbf{\epsilon}\) is skewness.  
Non-orthogonality is defined as the angle between vector \((\overrightarrow{c})\), which connects the center points of two cells, and normal vector \((\overrightarrow{A})\), at the center point M of the intersection of two cells. Non-orthogonality is calculated, as shown in Equation (4).  
\[\mathbf{\Theta}=cos^{-1}\left(\frac{\overrightarrow{A}\cdot\overrightarrow{c} }{\overrightarrow{A}\times\left|\overrightarrow{c}\right|}\right) \tag{4}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Boundary Condition** & **Value** \\ \hline Time step & Steady state \\ Turbulence model & Standard \(k\)-\(\varepsilon\) \\ Inlet velocity & 3.0 m/s \\ Inlet temperature & 293.15 K \\ Bottom temperature & 303.15 K \\ Inlet turbulence kinetic energy & 0.1350 \\ Inlet turbulence dissipation rate & 0.0085 \\ Air density & Incompressible-Ideal gas \\ Gravitational acceleration & 9.81 m/s\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: The boundary condition of validation model.  
Figure 4: Estimation of skewness and non-orthogonality.  
where, \(\theta\) is non-orthogonality.  
Low mesh quality can affect the convergence and error of the entire CFD model, therefore skewness and non-orthogonality were evaluated based on the maximum value. The recommended grid quality in OpenFOAM is as follows: Maximum non-orthogonality (70\({}^{\circ}\) or less), maximum skewness (4.0 or less) [35].  
The accuracy of the simulation results was evaluated by analyzing the relative error rate with the ANSYS simulation results. As shown in Equation (5), the difference between the CFD model created with the proposed method with OpenFOAM and the ANSYS analysis results was evaluated.  
\[e=\ \frac{|v_{a}-\ v_{t}|}{v_{a}}\ \times 100\% \tag{5}\]  
where, \(e\) is percent error, \(v_{a}\) is the value of ANSYS simulation, and \(v_{t}\) is the value of the proposed method. An overview of abbreviations and parameters can be found in Appendix A.  
The relative error rates were calculated for the average temperature and flow velocity for each target. The validation was conducted by evaluating the error rate for the total volume and the error rate for each section height (0.5 m, 1.0 m, 1.5 m, 2.0 m). In the case of ANSYS simulation, an analysis was performed with the CFD model for the original shape of the target building.