A Finite-Volume method for compressible non-equilibrium two-phase flows in networks of elastic pipelines using the Baer–Nunziato model

Abstract A novel Finite-Volume scheme for the numerical computations of compressible two-phase flows in pipelines is proposed for the fully non-equilibrium Baer–Nunziato model. The present FV approach is the extension of the method proposed in Daude and Galon (2018) in the context of the Euler equations to the Baer–Nunziato model. In addition, proper approximations of the non-conservative terms are proposed to consider jumps of volume fraction as well as jumps of cross-section in order to respect uniform pressure and velocity profiles preservation. In particular, focus is given to the numerical treatment of abrupt changes in area and to networks wherein several pipelines are connected at junctions. The proposed method makes it possible to avoid the use of an iterative procedure for the solution of the junction problem. The present approach can also deal with general Equations Of State. In addition, the fluid–structure interaction of compressible fluid flowing in flexible pipes is also considered. The proposed scheme is then assessed on a variety of shock-tubes and other transient flow problems and experiments demonstrating its capability to resolve such problems efficiently, accurately and robustly.