Central Schemes for Non Conservative Hyperbolic Systems

In this work we present a new approach to the construction of high order finite volume central schemes on staggered grids for general hyperbolic systems, including those not admitting a conservation form. The method is based on finite volume space discretization on staggered cells, central Runge--Kutta time discretization, and integration over a family of paths, associated to the system itself, for the generalization of the method to nonconservative systems. Applications to the one- and two-layer shallow water models as prototypes of systems of balance laws and systems with source terms and nonconservative products, respectively, will be illustrated. Read More: http://epubs.siam.org/doi/abs/10.1137/110828873