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This paper is concerned with the development of high order meth- ods for the numerical approximation of one-dimensional nonconservative hy- perbolic systems. In particular, we are interested in high order extensions of the generalized Roe methods introduced in (36), based on WENO reconstruc- tion of states. We also investigate the well-balance properties of the resulting schemes. Finally, we will focus on applications to shallow-water systems.

mathematics of computation

High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems