Air entrainment in transient flows in closed water pipes: a two-layer approach.

Christian Bourdarias (1) , Mehmet Ersoy (1) , Stéphane Gerbi (1)

1 LAMA - Laboratoire de Mathématiques

In this paper, we first construct a model for transient free surface flows that takes into account the air entrainment by a sytem of 4 partial differential equations. We derive it by taking averaged values of gas and fluid velocities on the cross surface flow in the Euler equations (incompressible for the fluid and compressible for the gas). Then, we propose a mathematical kinetic interpretation of this system to finally construct a well-balanced kinetic scheme having the properties of conserving the still water steady state and possesing an energy. Finally, numerical tests on closed uniforms water pipes are performed and discussed.

Mots clés: Two-layer model; pressurised air flows; free surface flows; well-balanced kinetic scheme; non conservative product.; non conservative product

Domaines: Equations aux dérivées partielles [math.AP]

Christian Bourdarias, Mehmet Ersoy, Stéphane Gerbi. Air entrainment in transient flows in closed water pipes: a two-layer approach.. 2009. ⟨hal-00421402v1⟩