## 6 Conclusions and Future Activities  
In the present work, an iterative Global/Local procedure has been implemented in a finite element commercial code, in order to study the thermo-mechanical behavior of the cooling channel of a liquid rocket engine thrust chamber. Typically, iterative and non-iterative Global/Local approaches have been employed in the past to study very narrow portions of the model where stress concentrations and plastic strains were expected; on the contrary, in the present work, the authors have investigated how the iterative approach works when the extent of nonlinear areas/volumes is very large if compared with the entire model considered. Then, for the test case chosen, the results have demonstrated the usefulness of the iterative Global/Local procedure--in fact, even considering very large local models, one iteration is needed to meet the chosen convergence criteria. This means that the elastic-plastic test-case under investigation is such that the effects of non-linearities affect the stress/strain fields of areas that are far away from nonlinear areas. Furthermore, the computational cost of a single numerical solution carried out adopting the Reference model is still higher than the computational cost needed to solve one iteration of the Global/Local analysis. Then, the adoption of the iterative approach is advantageous and allows for a significant computation time saving. That said, when the interface between the global and the local model is inside the nonlinear portion of the model, several iterations are needed to reach convergence; then, the approach is no longer advantageous.  
The authors have also investigated how the discretization of both Global and Local models at their interface affects the accuracy and the computation time.  
The results of the test cases examined have shown that, when the local models are significantly larger than the local nonlinear areas, the choice of non-conformal meshes could allow for just a 5% computation time saving if compared with that needed for a configuration with conformal mesh.  
As a future activity, the authors are planning to implement more sophisticated coupling techniques that can handle very different meshes at the interface between Global and Local models, allowing for additional computation time savings. Furthermore, the present Global/Local procedure could become more convenient if nonlinear models, taking into account creep and viscoplastic phenomena, are considered.  
Conceptualization, M.F., R.C.; Data curation, M.F., M.L. and R.C.; Investigation, M.F., M.L. and R.C.; Writing--original draft, M.F. and R.C. All authors have read and agreed to the published version of the manuscript. This research received no external funding. This research has been supported by the Italian Ministry of University and Research (MIUR), in the frame of the Hyprob Program. The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Nodes:** & \multicolumn{2}{c}{**Nodes:**} & & & & \\ \multirow{2}{*}{**Local**} & **Global** & **Global** & & & **CPU Time** & **CPU Time** \\  & **Global** & **Coarse** & **Coarse** & **Local Model** & **(Conformal** & **Non–** & **Coarse** \\
**Models** & **Model** & **(Non–** & **Local Model** & **Mesh)** & **Conformal** & **Model**) \\  & **(Conformal** & **Non–** & **Conformal** & **(s)** & **(s)** & **(s)** \\  & **Mesh** & **Mesh** & & & & \\ \hline y = 0.5 & 4800 & 4700 & 10,000 & 50 & 38 & 150 \\ y = 0.9 & 4600 & 3864 & 15,000 & 26 & 22 & 150 \\ y = 1.2 & 4600 & 3864 & 17,500 & 50 & 48 & 150 \\ y = 1.5 & 4600 & 3864 & 18,200 & 52 & 50 & 150 \\ y = 1.8 & 4600 & 3864 & 18,800 & 53 & 50 & 150 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Computation time—Three–dimensional Global/Local analyses.