In the context of sodium cooled Generation IV reactors, high performance computations of severe accidents require domain decomposition methods able to handle non-conforming mesh interfaces. Such interfaces allow local mesh refinement in sensitive regions while keeping the mesh coarser elsewhere, reducing computational costs without losing accuracy. Several families of methods exist, including Schwarz methods, Schur complement formulations and Lagrange multipliers approaches including Mortar methods, but few results deal with the coupling of nonlinear operators across non-conforming interfaces in finite volume schemes. This work focuses on developing a non-conforming coupling method into the severe accident simulation code SIMMER V (CEA–JAEA). Since SIMMER-V solves the Euler or Navier–Stokes equations, its hyperbolic operators must also be coupled across non-conforming interfaces. For hyperbolic systems, the propagation direction is generally known locally along the interface, which usually makes the coupling clear, but an ambiguity may arise when a locally finer mesh assigns different directions to the same coarse cell. However, with nonlinear operators and non matching meshes, interpolating the solution leads to inconsistencies, making it necessary to impose the Neumann interface condition through an appropriate flux interpolation. This approach has already been implemented and validated in a dedicated script. The Navier–Stokes equations also involve nonlinear parabolic operators and a global elliptic system from the pressure correction step. To handle these operators, we investigate how existing coupling methods can be adapted to simultaneously treat non matching grids, nonlinear operators, and finite volume schemes. Several strategies are tested by combining explicit or implicit time integration with explicit or implicit interface coupling. All combinations are evaluated in terms of stability, conservation and computational cost in order to identify the most suitable approaches for these types of problems, with the goal of integrating them into SIMMER-V software.