A kinetic scheme for pressurised flows in non uniform closed water pipes

The aim of this paper is to present a kinetic numerical scheme for the computations of transient pressurised flows in closed water pipe with non uniform sections. Firstly, we detail the derivation of the mathematical model in curvilinear coordinates and we performe a formal asymptotic analysis. The obtained system is written as a conservative hyperbolic partial differential system of equations. We obtain a kinetic interpretation of this system and we build the corresponding kinetic scheme based on an upwinding of the source terms written as the gradient of a “pseudo altitude”. The validation is lastly performed in the case of a water hammer in an uniform pipe: we compare the numerical results provided by an industrial code used at EDF-CIH (France), which solves the Allievi equations (the commonly used equation for pressurised flows in pipe) by the method of characteristics, with those of the kinetic scheme. To validate the contracting or expanding cases, we compare the presented technique to the equivalent pipe method in the case of an immediate flow shut down in a quasi-frictionless cone-shaped pipe.