文档介绍：J. Fluid Mech. (2001), vol. 431, pp. 239–271. Printed in the United Kingdom 239
c 2001 Cambridge University Press
A multiphase model pressible flows with
interfaces, shocks, detonation waves and
cavitation
By RICHARD SAUREL AND OLIVIER LEMETAYER
IUSTI, Universite´ Aix Marseille I, 5 rue E. Fermi, 13453 Marseille Cedex 13, France and
INRIA, Project SMASH, Marseille, France
e-mail: richard/******@-
(Received 31 January 2000 and in revised form 28 September 2000)
pressible multiphase unconditionally hyperbolic model is proposed. It is able
to deal with a wide range of applications: interfaces pressible materials,
shock waves in condensed multiphase mixtures, homogeneous two-phase flows (bub-
bly and droplet flows) and cavitation in liquids. Here we focus on the generalization
of the formulation to an arbitrary number of fluids, and to mass and energy transfers,
and extend the associated Godunov method.
We first detail the specific problems involved in putation of thermodynamic
interface variables when dealing pressible materials separated by well-defined
interfaces. We then address one of the major problems in the modelling of detonation
waves in condensed energetic materials and propose a way to suppress the mixture
equation of state. We then consider another problem of practical importance related
to high-pressure liquid injection and associated cavitating flow. This problem involves
the dynamic creation of interfaces. We show that the multiphase model is able to
solve these very different problems using a unique formulation.
We then develop the Godunov method for this model. We show how the non-
conservative terms must be discretized in order to fulfil the interface conditions.
Numerical resolution of interface conditions and partial equilibrium multiphase mix-
tures also requires the introduction of infinite relaxation terms. We propose a way
to solve them in the context of an arbitrary number of fluids. This is of particu