In this paper, we will report our recent efforts to apply a Schur complement method for nonlinear hyperbolic problems. We use the finite volume method and an implicit version of the Roe approximate Riemann solver. With the interface variable introduced in Dao et al. (A Schur complement method for compressible Navier-Stokes equations. In: Proceedings of the 20th International Conference on Domain Decomposition Methods, 2011) in the context of single phase flows, we are able to simulate two-fluid models (Ndjinga et al., Nucl. Eng. Des. 238, 2008) with various schemes such as upwind, centered or Rusanov. Moreover, we introduce a scaling strategy to improve the condition number of both the interface system and the local systems. Numerical results for the isentropic two-fluid model and the compressible Navier-Stokes equations in various 2D and 3D configurations and various schemes show that our method is robust and efficient. The scaling strategy considerably reduces the number of GMRES iterations in both interface system and local system resolutions. Comparisons of performances with classical distributed computing with up to 218 processors are also reported.