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

Christian Bourdarias (1) , Stéphane Gerbi (1) , Mehmet Ersoy (2)

1 LAMA - Laboratoire de Mathématiques
2 BCAM - Basque Center for Applied Mathematics

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.

Mots clés: Finite volume scheme; Kinetic scheme; conservative source terms; non-conservative source terms; friction.; friction

Domaines: Equations aux dérivées partielles [math.AP]

Christian Bourdarias, Stéphane Gerbi, Mehmet Ersoy. A kinetic scheme for transient mixed flows in non uniform closed pipes: a global manner to upwind all the source terms. Journal of Scientific Computing, 2011, 48 (1-3), pp. 89-104. ⟨10.1007/s10915-010-9456-0⟩. ⟨hal-00434321v2⟩