The aim of this paper is to present a kinetic numerical scheme for the
computations of transient pressurised flows in closed water pipes with variable
sections. Firstly, we detail the derivation of the mathematical model in
curvilinear coordinates under some hypothesis and we performe a formal
asymptotic analysis. Then the obtained system is written as a conservative
hyperbolic partial differential system of equations, and we recall how to
obtain the corresponding kinetic formulation based on an upwinding of the
source term due to the "pseudo topography" performed in a close manner
described by Perthame and al
