Dimension reduction for incompressible pipe and open channel flow including friction. (English) Zbl 1363.76004

Ersoy, Mehmet

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, November 18–21, 2015. In honor of the birthday anniversaries of Ivo Babuška (90), Milan Práger (85), and Emil Vitásek (85). Prague: Czech Academy of Sciences, Institute of Mathematics (ISBN 978-80-85823-65-3). 17-33 (2015).

This paper presents a formal derivation of a 1D pipe flow equation from the incompressible Navier-Stokes system with general wall friction and free surface. The model finds many engineering applications such as storm sewers, waste or supply pipes in hydroelectric installations.
For the entire collection see [Zbl 1329.00187].

Reviewer: Jan Stebel (Liberec)

MSC:

76B07	Free-surface potential flows for incompressible inviscid fluids
65M08	Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M75	Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
76M12	Finite volume methods applied to problems in fluid mechanics
76M28	Particle methods and lattice-gas methods
76D05	Navier-Stokes equations for incompressible viscous fluids

Keywords:

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