  The aim of this paper is to present a kinetic numerical scheme for the
computations of transient pressurised flows in closed water pipes. Firstly, we
detail the mathematical model written as a conservative hyperbolic partial
differentiel system of equations, and the we recall how to obtain the
corresponding kinetic formulation. Then we build the kinetic scheme ensuring an
upwinding of the source term due to the topography performed in a close manner
described by Perthame et al. using an energetic balance at microscopic level
for the Shallow Water equations. The validation is lastly performed in the case
of a water hammer in a uniform pipe: we compare the numerical results provided
by an industrial code used at EDF-CIH (France), which solves the Allievi
equation (the commonly used equation for pressurised flows in pipes) by the
method of characteristics, with those of the kinetic scheme. It appears that
they are in a very good agreement.

Analysis of PDEs;Numerical Analysis;Classical Physics