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Charles Demay (EDF)
This work is dedicated to the modelling of air/water flows in pipes. As a 1rst
step, a new 1D model is proposed to deal with the stratified regime. The starting point is the
2D Isentropic Euler set of equations for phase k where the classical hydrostatic assumption
is made for water (k = 1) while the gravitational ects are neglected for air (k = 2). The
main difference with the models issued from the classical literature is that water as well as
air are assumed compressible. In that framework, an averaging process across the layer depth
results in a fiveequation system where the hydrostatic constraint has been introduced in an
original manner. Closure laws for interfacial terms and source terms are provided following an
entropy inequality and the overall model is hyperbolic with non conservative terms. Therefore,
the definition and uniqueness of jump conditions is studied carefully and acquired. Regarding
the Riemann problem associated with the homogeneous problem, the nature of characteristic
fields and the corresponding Riemann invariants are exhibited. Positivity is also obtained for
heights and densities.

