Abstract
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.
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