We present a general framework for high-order hierarchical dynamic domain decomposition methods for the Boltzmann equation based on moment realizability matrices, a concept introduced by Levermore, Morokoff and Nadiga. This criterion is used to dynamically partition the two-dimensional spatial domain into two main regimes: the Euler regime, and the kinetic regime. The key advantage of this approach lies in the use of Euler equations in regions where the flow is near hydrodynamic equilibrium, and the Boltzmann equation where strong non-equilibrium effects dominate, such as near shocks and boundary layers. This allows for both high accuracy and significant computational savings, as the Euler solver is considerably cheaper than the kinetic Boltzmann model. We have extended this general framework to different contexts: three levels domain decomposition method (Euler Equations, ES-BGK operator and full hard sphere Boltzmann operator), two different multi-species models of the gas mixtures Boltzmann equation, and on unstructured meshes. We implement a coupling mechanism between the two regimes capable of preserving the high-order accuracy of both Euler and kinetic solvers, and we use state-of-the-art numerical techniques. This combination enables robust and scalable simulations of multi-scale kinetic flows with complex geometries in various settings and scenarios. Joint work with Lorenzo Pareschi (University of Ferrara & Heriot-Watt University), Thomas Rey (Université Cote-d'Azur) and Tommaso Tenna (Université Cote-d'Azur & University of Rome "La Sapienza").