We assess the performance of domain decomposition methods for two types or reduced order model (ROM): projection-based reduced order model (pROM) and a collocation-based reduced order model (cROM)[1]. The equations are solved in a subspace determined with proper orthogonal decomposition (POD) of dimension p. From the pROM we use a Petrov-Galerkin method based on a hyper-reduction technic similar to ECSW[2] to compute the non-linear term. The cROM solves the high-fidelity scheme only at a subset of the mesh nodes, determined by the NNLS algorithm tuned to recover the coefficients within the POD subspace. Domain decomposition consists in slicing the physical domain into subdomains parts, and then build separate ROMs on each subdomain. This allows us to run multifidelity (high fidelity on one subdomain and ROM with a lower fidelity on another) simulations, and to test iterative local training strategies. The iterative local training strategy starts with a regular simulation on a coarse grid for the whole domain. This initial solution determines a reduced order basis for the next simulations. Finally, we employ a multifidelity simulation iterating on each subdomain to obtain a ROM on each subdomain for a finer grid at lower computational cost. We assess the potential of these methods by investigating the approximation of the unsteady compressible Euler equations in 1D, and to a stationary 2D problem. The results show that the multifidelity approach is numerically stable, accurate, and for a given computational budget, it reaches higher accuracy on a single domain as compared to a high-fidelity simulation on the whole domain. REFERENCES [1] Michel Bergmann, Michele Giuliano Carlino, Angelo Iollo. Model order reduction using a collocation scheme on chimera meshes: addressing the Kolmogorov N-width barrier. 2024. hal-04705778 [2] Sebastian Grimberg, Charbel Farhat, Radek Tezaur, and Charbel Bou-Mosleh. Mesh sampling and weighting for the hyperreduction of nonlinear Petrov-Galerkin reduced-order models with local reduced-order bases. International Journal for Numerical Methods in Engineering, 122(7) :1846-1874, 2021