Dimension reduction for incompressible pipe and open channel flow including friction

Mehmet Ersoy (1)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134

We present the full derivation of a one-dimensional free surface pipe or open channel flow model including friction with non constant geometry. The free surface model is obtained from the three-dimensional incompress-ible Navier-Stokes equations under shallow water assumptions with prescribed " well-suited " boundary conditions.

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

Domaines: Equations aux dérivées partielles [math.AP]

Mehmet Ersoy. Dimension reduction for incompressible pipe and open channel flow including friction. Conference Applications of Mathematics 2015, in honor of the 90th birthday of Ivo Babuška and 85th birthday of Milan Práger and Emil Vitásek , J. Brandts and S. Korotov and M. Křížek and K. Segeth and J. Ŝístek and T. Vejchodský, Nov 2015, Institute of Mathematics CAS, Prague, France. pp.17-33. ⟨hal-00908961v2⟩