A Schur Complement Method for Compressible Two-Phase Flow Models Thu-Huyen DAO 1,2 , Michael NDJINGA 1 , and Fr´ ed´ eric MAGOUL ` ES 2 Abstract 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 [4] in the context of single phase flows, we are able to simulate two- fluid models ([12]) 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 compresible 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. Key words: Compressible flows, Riemann solver, Schur complement. 1 Introduction Computations of complex two-phase flows are required for the safety analysis of nuclear reactors. These computations keep causing problems for the development of best estimate computer codes dedicated to design and safety studies of nuclear reactors. Moreover, we often need to find the long-term behavior of the system. In these cases, implicit schemes are proven very efficient. Unfortunately, for implicit schemes, after the discretization, we need to solve a nonlinear system A U = b. This task is computationally expensive in particular since the matrix A is usually non-symmetric and very ill-conditioned. It is therefore necessary to find an efficient preconditioner. When the size of the system is large, the parallel resolution on multiple processors is essential to obtain reasonable computation times. Currently in the thermal hydraulic code, FLICA-OVAP (see [7]), the matrix A and the right hand side b are stored on multiple processors and the system is solved in parallel with a Krylov solver with a classical incomplete factorization preconditioner. Unfortunately, the parallel pre- conditioners of FLICA-OVAP only perform well on a few processors. In contrast, if we want to increase the number of processors these parallel preconditioners per- 1: CEA–Saclay, DEN, DM2S, STMF, LMEC, F–91191 Gif–sur–Yvette, France · 2: Appl. Mat. and Syst. Lab., Ecole Centrale Paris, 92295 Chˆ atenay–Malabry, France frederic.magoules@hotmail.com 1