A rough finite volume scheme for modeling two-phase flow in a pipeline

Abstract This paper deals with the resolution of the hyperbolic system of conservation laws which arises when modeling two-phase flow in an oil and gas pipeline. The model considered here is of the drift–flux type where the slip velocity between the two phases is given by a hydrodynamic model that accounts for the different flow regimes. The complexity of the closure relations prevents us from using classical numerical schemes such as Godunov or Roe's scheme. We propose another finite volume scheme, more rough for which the numerical flux is written as a centered scheme stabilized by a viscous term. The system considered has also the characteristic of having eigenvalues which are of very different orders of magnitude. We present a time discretization which is explicit for the “slow waves” and implicit for the “fast waves”. It allows the use of a time step which is governed only by the “slow waves” and keeps a good precision for these waves.