A Schur Complement Method for Compressible Two-Phase Flow Models

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 twofluid 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 twofluid 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.