  We present a numerical kinetic scheme for an unsteady mixed pressurised and
free surface model. This model has a source term depending on both the space
variable and the unknown, U, of the system. The source term is composed by a
topography, a section variation, a curvature (also called corrective) and a
friction term. Using the Finite Volume and Kinetic (FVK) framework, we propose
an approximation of the source terms following the principle of interfacial
upwind with a kinetic interpretation: the source term is not treated as a
volumic term, but included in the numerical fluxes. Then, several numerical
tests are presented.
