%0 Journal Article
%T A kinetic scheme for transient mixed flows in non uniform closed pipes: a global manner to upwind all the source terms
%A Christian Bourdarias
%A Mehmet Ersoy
%A St¨¦phane Gerbi
%J Mathematics
%D 2009
%I arXiv
%R 10.1007/s10915-010-9456-0
%X 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.
%U http://arxiv.org/abs/0911.4269v2