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

This paper deals with the resolution of the hyperbolic system of conservati on laws which arises when modeling two-phase flow in an oil and gas pipelin e. The model considered here is of the drift-flux type where the slip veloc ity between the two phases is given by a hydrodynamic model that accounts f or the different flow regimes. The complexity of the closure relations prev ents us from using classical numerical schemes such as Godunov or Roe's sch eme. We propose another finite volume scheme, more rough for which the nume rical flux is written as a centered scheme stabilized by a viscous term. Th e system considered has also the characteristic of having eigenvalues which are of very different orders of magnitude. We present a time discretizatio n 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. (C) 1999 Elsevier Science Ltd . All rights reserved.