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

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.