6533b7d2fe1ef96bd125f52f
RESEARCH PRODUCT
A multiscale approach to liquid flows in pipes I: The single pipe
Ingenuin GasserArne RoggensackUlf TeschkeAndrea CorliMaria Lukacova-medvidovasubject
PhysicsPipe flowWater hammerApplied MathematicsTime evolutionMechanicsPipe flow; Saint-Venant equations; multiscale analysis; water-hammer; pressure wavesmultiscale analysisPipe flowwater-hammerComputational MathematicsNonlinear systemHydraulic headFlow (mathematics)pressure wavesBarotropic fluidSaint-Venant equationsShallow water equationsSimulationdescription
Abstract In the present paper we study the propagation of pressure waves in a barotropic flow through a pipe, with a possibly varying cross-sectional area. The basic model is the Saint–Venant system. We derive two multiscale models for the cases of weak and strong damping, respectively, which describe the time evolution of the piezometric head and the velocity. If the damping is weak, then the corresponding first-order hyperbolic system is linear but contains an additional integro-differential equation that takes into account the damping. In the case of strong damping, the system is nonlinear. The full and multiscale models are compared numerically; we also discuss results obtained by a largely used commercial software. The numerical experiments clearly demonstrate the efficiency of the multiscale models and their ability to yield reliable numerical approximations even for coarse grids, that is not the case for the full model.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-10-01 |