A conservative model for unsteady flows in deformable pipes and its implicit second order finite volume discretisation

Christian Bourdarias (1) , Stéphane Gerbi (1)

1 LAMA - Laboratoire de Mathématiques

We present a one dimensional model for compressible flows in a deformable pipe which is an alternative to the Allievi equations and is intended to be coupled in a ”natural way” with the shallow water equations to simulate mixed flows. The numerical simulation is performed using a second order linearly implicit scheme adapted from the Roe scheme. The validation is performed in the case of water hammer in a rigid pipe: we compare the numerical results provided by an industrial code with those of our spatial second order implicit scheme. It appears that the maximum value of the pressure within the pipe for large CFL numbers and a coarse discretisation is accurately computed.

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

Christian Bourdarias, Stéphane Gerbi. A conservative model for unsteady flows in deformable pipes and its implicit second order finite volume discretisation. Computers and Fluids, 2008, 37, pp.1225-1237. ⟨hal-00387195⟩