A kinetic formulation for a model coupling free surface and pressurised flows in closed pipes

Christian Bourdarias (1) , Stéphane Gerbi (1) , Marguerite Gisclon (1)

1 LAMA - Laboratoire de Mathématiques

The aim of this paper is to present a kinetic formulation of a model for the coupling of transient free surface and pressurised flows. Firstly, we revisit the system of Saint-Venant equations for free surface flow: we state some properties of Saint-Venant equations, we propose a kinetic formulation and we verify that this kinetic formulation leads to a {\it Gibbs equilibrium } that minimises (in some general case) an energy and preserves the still water steady state. Secondly, we propose a model for pressurised flows in a Saint-Venant-like conservative formulation. We then propose a kinetic formulation and we verify that this kinetic formulation leads to a Gibbs equilibrium that minimises in any case an energy and preserves the still water steady state. Finally, we propose a dual model that couples these two types of flow.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]

Christian Bourdarias, Stéphane Gerbi, Marguerite Gisclon. A kinetic formulation for a model coupling free surface and pressurised flows in closed pipes. Journal of Computational and Applied Mathematics, 2008, 218 (2), pp.522-531. ⟨hal-00387199⟩