A free surface model for incompressible pipe and open channel flow.

Mehmet Ersoy (1)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134

We present the full derivation of a free surface pipe or open channel model including friction, changes of section and changes of slope/topography. This 1D free surface model (also named \textbf{FS}-model) is obtained from the incompressible 3D Navier-Stokes equation under shallow water assumptions with well-suited boundary conditions. It was introduced in the general framework of unsteady mixed flows in closed water pipes and is largely used by the engineers community.

Mots clés: free surface flow; incompressible Navier-Stokes; shallow water approximation; hydrostatic approximation; closed water pipe; open channel; friction; viscosity

Domaines: Equations aux dérivées partielles [math.AP]

Mehmet Ersoy. A free surface model for incompressible pipe and open channel flow.. 2013. ⟨hal-00908961v1⟩