## 1 Introduction  
The present work has been developed in the framework of the Hyprob project, funded by the Italian Ministry of University and Research (MIUR) and led by the Italian Aerospace Research Center (CIRA) [1]. The aim of the project was to design, manufacture and test a 3 tons thrust chamber adopting liquid methane as refrigerant and fuel and liquid oxygen as an oxidizer [2; 3; 4; 5; 6]. The present study focus on the final Demonstrator, a regeneratively cooled thrust chamber. The Demonstrator comprises an inner structure made of a copper alloy (CuCrZr), and an external cold structure made of electrodeposited nickel (Figure 1). Carrying out a thermomechanical analysis of the cooling channel can be very demanding from a computational point of view, since nonlinear phenomena, such as plasticity, and time-dependent phenomena (e.g., creep) can come into play [7; 8; 9; 10; 11; 12]. Consequently, there is a strong need to adopt simplified models or, in turn, numerical procedures that can save computation time. A common approach is based on a Global/Local sub-modelling that makes it possible to restrict the nonlinear analysis only to the areas where plastic strains are envisaged, without affecting the computational burden inherent the global model resolution [13, 14]. Generally, two separate finite element analyses on two separate models are conducted: a Global linear model with a coarse mesh and a Local nonlinear model with a fine mesh. A one-way approach is taken, where the displacements at the interface between the Global and Local models, evaluated by a finite element linear analysis of the Global model, are transferred to the Local nonlinear model as boundary conditions. Generally, in such an approach the Global model results affect the Local model analysis and not vice versa [14], but [PERSON] et al. proposed a two-way approach with the aim to improve the level of accuracy of the numerical results [15]. In the latter approach, the results of the Local model, in terms of nodal forces at the boundaries with the Global model, are subtracted from the nodal forces evaluated by means of the Global analysis and then applied as extra boundary conditions in the subsequent Global analyses. After a few iterations, the forces to apply at the boundary tend to zero; this means that convergence has been reached, as also demonstrated by a comparison with the results of a FEM Reference model. For the latter model, the mesh in the submodelled area exactly reproduces the mesh of the Local model, whereas the remainder of the domain reproduces that of the Global coarse model. Even if in this work FEM is used, such a submodelling procedure can also be based on the Boundary Element Method (BEM) [16, 17, 18]. The two-way approach is very useful and efficient when local plasticization is envisaged, whereas one-way approaches could lead to very approximate results, since the nonlinear effects of the Local model on the Global one are not effectively taken into account. Such a procedure was employed only for conformal meshes in [15], namely the nodes of the Global and Local models are coincident at their interface. In this work, such constraints were removed, with the consideration of non-conformal meshes. The iterative technique has already been applied with a good success rate in many engineering fields, such as the study of local plasticity, where geometrical refinements can also be taken into account, such as the analysis of crack propagation [19] and so on. Recently, [PERSON] et al. adopted the  
Figure 1: Schematic representation of a liquid rocket engine thrust chamber. same algorithm and provided some guidelines to minimize the number of iterations needed to reach convergence [20]; furthermore, they developed an overlapping version of the method with the aim to use the algorithm for fully non-conformal meshing.