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Pré-Publication, Document De Travail Année : 2008

A mathematical model for unsteady mixed flows in closed water pipes

Christian Bourdarias
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Stéphane Gerbi
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Résumé

We present the derivation of a new unidirectionnal model for unsteady mixed flows in non uniform closed domains. We introduce a local reference frame to take into account the local perturbation caused by the changes of section and slope. Then an asymptotic analysis is performed to obtain a model for the free surface flow and another for the pressurised flow. By coupling these models through the transition points by the use of a common set of variables and a suitable pressure law, we obtain a simple formulation called PFS-model close to the shallow water equations with source terms. It takes into account the changes of section and the slope variation in a continuous way through transition points.
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Dates et versions

hal-00342745 , version 1 (28-11-2008)
hal-00342745 , version 2 (04-05-2009)
hal-00342745 , version 3 (06-11-2009)

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Christian Bourdarias, Mehmet Ersoy, Stéphane Gerbi. A mathematical model for unsteady mixed flows in closed water pipes. 2008. ⟨hal-00342745v1⟩
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