A kinetic scheme for transient mixed flows in non uniform closed pipes: a global manner to upwind all the source terms

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.