# Effects of Turbulence Modeling on the Simulation of Wind Flow over Typical Complex Terrains
## 4 Results and Discussions  
In this paper, we propose two modified RANS turbulence models. The main purpose of this paper is to evaluate the performance of different RANS turbulence models, including the standard SST \(k\)-\(\omega\) model, the standard linear pressure-strain RSM model, and innovative variants of these two models, in simulating the wind flow over complex terrain by comparing the numerical results with the experimental observations. The main study is to investigate the maintenance characteristics of the velocity and TKE upstream of the computational domain, and the accuracy of the simulation results of the velocity and TKE around the mountain, using multiple measurement points to make a comprehensive comparison from streamwise and vertical directions. \begin{table}
\begin{tabular}{c c} \hline \hline
**Location** & \multicolumn{2}{c}{**Boundary Conditions**} \\ \hline \begin{tabular}{c} Inlet boundary \\ (the inlet wind speed and turbulence profile are shown on \\ the right when \(z<H_{\text{abl}}\), and \(u\), \(k\), \\ and \(\varepsilon\) are constant when \(z\geq H_{\text{abl}}\)) \\ \end{tabular} & \begin{tabular}{c} Velocity inlet: \\ \(U=\frac{u_{s}}{\varepsilon}(\frac{z+z_{0}}{z_{0}})-\overline{u^{\prime}u^{ \prime}}=u_{s}^{2}(1-\frac{z}{H_{\text{abl}}})^{2}k=\frac{u_{s}^{2}}{\sqrt{C_{ s}}}(1-\frac{z}{H_{\text{abl}}})^{2}\) \\ \end{tabular} & \begin{tabular}{c} \(U^{2}=\frac{u_{s}}{\varepsilon}(1-\frac{z}{H_{\text{abl}}})^{2}\)\(\omega=\frac{u_{s}}{\sqrt{C_{s}}(z+z_{0})}\)\(\overline{u^{\prime}u^{\prime}}=\frac{2}{5.466}\)\(\bullet\) \\ \end{tabular} \\ \begin{tabular}{c} Outlet boundary \\ Lateral boundary \\ Upper boundary \\ Lower boundary \\ \end{tabular} & \begin{tabular}{c} Outflow: \(\frac{u}{\varepsilon}(U_{x},U_{y},U_{z},k,\varepsilon)=0\)\(U_{y}=0\) \\ \end{tabular} \\ \begin{tabular}{c} Upper boundary \\ Lower boundary \\ \end{tabular} & \begin{tabular}{c} Symmetry: \(\frac{\partial}{dx}(U_{x},U_{y},U_{z},k,\varepsilon)=0\)\(U_{z}=0\) \\ \end{tabular} \\ \
\begin{tabular}{c} Lower boundary \\ \end{tabular} &
\begin{tabular}{c} Modify wall function: \(K_{\text{S}}=0.95z_{p}\)\(C_{\text{S}}=\frac{9.793z_{0}}{0.95(z+z_{p})}\) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Boundary conditions of the basic calculation model; \(z\) is the height above the ground. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Test Cases** & \(\mathbf{u_{s}}\) **[m/s]** & \(\mathbf{H_{\text{abl}}}\) **[m]** \\ \hline Case 1: 3D hill in wind tunnel & 0.21 & 0.419 \\ Case 2: Askervein hill & 0.612 & 850 \\ Case 3: Bolund island (270\({}^{\circ}\)) & 0.469 & 644 \\ Case 4: Bolund island (239\({}^{\circ}\)) & 0.3559 & 494 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Inflow conditions for the four test cases: \(u_{s}\), friction velocity; \(H_{\text{abl}}\), the atmospheric boundary layer height; \(\kappa\), the von Kármán constant (\(\approx\)0.4). \begin{table}
\begin{tabular}{l l} \hline \hline
**System** & \multicolumn{2}{c}{**Numerical Schemes**} \\ \hline Solver & Ansys Fluent 19.0. \\  & SIMPLE algorithm for the pressure–velocity coupling, Green–Gauss \\ Solving algorithm & node-based approach for the calculation of gradients, the \\  & second-order upwind schemes for velocity and turbulence, and the \\  & PRESTO! scheme for pressure. \\ Convergence criteria & Below \(1\times 10^{-6}\) for all residuals. \\  & Convergence is achieved in 963 and 1699 CPU hours for Case 1 with \\  & the two-equation model and the RSM model, 358 and 759 CPU hours for Case 2, and 2999 and 5695 CPU hours for Cases 3 and Case4, \\  & respectively.