 
Summary: Journal of Computational Physics 150, 425467 (1999)
Article ID jcph.1999.6187, available online at http://www.idealibrary.com on
AMultiphaseGodunovMethodforCompressible
Multifluid and Multiphase Flows
Richard Saurel and R´emi Abgrall
IUSTI, CNRS UMR 6595, 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France; and
Universit´e de Bordeaux I, 351 cours de la Lib´eration, 33405 Talence, France
Email: richard@iusti.univmrs.fr and abgrall@math.ubordeaux.fr
Received June 9, 1998; revised December 14, 1998
We propose a new model and a solution method for twophase compressible flows.
The model involves six equations obtained from conservation principles applied to
each phase, completed by a seventh equation for the evolution of the volume fraction.
This equation is necessary to close the overall system. The model is valid for fluid
mixtures, as well as for pure fluids. The system of partial differential equations
is hyperbolic. Hyperbolicity is obtained because each phase is considered to be
compressible. Two difficulties arise for the solution: one of the equations is written
in nonconservative form; nonconservative terms exist in the momentum and energy
equations. We propose robust and accurate discretisation of these terms. The method
solves the same system at each mesh point with the same algorithm. It allows the
simulation of interface problems between pure fluids as well as multiphase mixtures.
