## 5 Results and Discussion
### Two-Dimensional Global/Local Analyses  
The maximum temperature value (740 K) is detected on the inner wall of the cooling channel, which is exposed to the hot combustion gases (see Figures 9 and 10). Figure 10 shows the Von Mises stresses and the Equivalent Plastic Strains contour plots for the Reference Model: as expected, plastic strains are detected only in the area enclosed by the red rectangle. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Temperature (K)** & **Density (kg/m\({}^{3}\))** & **Thermal Conductivity (W/mK)** & **Specific Heat (J/kgK)** & **Thermal Expansion Coefficient (1/K)** \\ \hline
300 & 8913 & 90 & 444 & \(12.2\times 10^{-6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Physical properties of the electrodeposited Nickel. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Temperature (K)** & **E (Gpa)** & **Yield Stress (MPa)** & **Ultimate Stress (MPa)** & **Poisson’s Ratio** \\ \hline
28 & 193 & 344 & 551 & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Mechanical properties of the electrodeposited Nickel. Trade-Off Analysis with Non-Conformal Meshes  
A trade-off analysis has been conducted varying the parameter \(\
u_{n}\) defined in Equation (14). Four values have been chosen for the analysis:  
1. \(\
u_{n}=0.5\)
2. \(\
u_{n}=0.70\)  
Figure 10: Von [PERSON] stress (left) and Equivalent plastic strain (right) contour plots—Reference Model. Figure 9: Temperature contour plot—Reference Model. \(\
u_{n}=0.85\)
4. \(\
u_{n}=1\)  
The configuration with \(\
u_{n}=1\) is representative of a Local Model with conformal mesh at the interface with the Global Model. In what follows, the results, in terms of \(\eta_{\varepsilon}\) and \(\eta_{\sigma}\), for all the values of \(\
u_{n}\) and for all the local models, will be shown with the aim to identify the value of \(\
u_{n}\) that guarantees a monotonic convergence towards the Reference Model corresponding values. Figure 11 shows the convergence history for all the local models considered: the number of iterations needed to reach convergence, under the same Local Model, for conformal and non-conformal meshes is very similar; for instance, for Local Model 1 the number of iterations sufficient to reach convergence is 9 for conformal meshes and 10 for non-conformal meshes. The variations of \(\eta_{\varepsilon}\) and \(\eta_{\sigma}\) vs. the current iteration for all the cases examined are shown in the next figures. In particular, Figure 11 shows that for Local Model 1 the improvement of the results accuracy by the iterative procedure vs. \"one-way\" approach (no iterations), is very similar for all the configurations examined; however, it is clear that only the configuration with \(\
u_{n}=0.85\) is such that \(\eta_{\varepsilon}\) values are monotonically convergent towards smaller values, while for the other configurations a minimum value is detected after 4-5 iterations (see Figure 12). Then, the configuration \(\
u_{n}=0.85\) is compared with the conformal mesh configuration (\(\
u_{n}=1\)), showing  
In general, it is evident that the adoption of the present iterative procedure allows for a significant decrease of \(\eta_{\epsilon}\) (from 14.5% to about 8% after only four iterations), while \(\eta_{\sigma}\) remains almost constant. Similar considerations can be made for the other Local Models. Figure 12: Global/Local performance with respect to the reference Model—comparison between different levels of non–conformal meshes—Local Model 1. Figure 13: Global/Local performance with respect to the reference Model—conformal mesh and optimal non–conformal mesh. With regard to Local Model 2, it is clear that \(\eta_{\varepsilon}\) values for all the configurations decrease to acceptable values after only 2-3 iterations (see Figure 14). On the other hand, the deviations from the Reference Model Von Mises stress values are very small. The configurations with \(\
u_{n}=0.85\) and \(\
u_{n}=0.7\) have a very similar behavior, monotonically convergent towards the Reference Model values.