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IMA Journal of Applied Mathematics 2003 68(6):595-620; doi:10.1093/imamat/68.6.595
© 2003 by Institute of Mathematics and its Applications
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Well-posedness of incompressible models of two- and three-phase flow

M. Louaked1, L. Hanich2 and C. P. Thompson2

1 Department de Mathématiques et Mécanique, Université de Caen, Campus II, Bd. Maréchal Juin, B P 5186, 14032 Caen, France 2 Applied Mathematics and Computing Group, School of Engineering, Cranfield University, UK

In this paper the Hadamard well-posedness of incompressible multiphase flow systems is addressed. We determine the hydrodynamic conditions under which these systems are hyperbolic, stable and possess a unique short-time solution provided the initial data are in an appropriate Sobolev space and the source terms in a class of sufficiently differentiable functions. An accurate and efficient numerical method coupled with an adaptive mesh strategy, for predicting the evolution of flow phenomena, is presented. Numerical predictions of transient- and steady-flow problems in pipelines are compared with available experimental data.

Keywords: holdup; hyperbolic system; pipeline; pseudo-differential operator; stratified; three-phase flow; two-phase; well-posedness.

Received 14 February 2002. Revised 21 November 2002.


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