  In this work we develop a new framework to deal numerically with
discontinuous solutions in nonconservative hyperbolic systems. First an
extension of the MOOD methodology to nonconservative systems based on Taylor
expansions is presented. This extension combined with an in-cell discontinuous
reconstruction operator are the key points to develop a new family of
high-order methods that are able to capture exactly isolated shocks. Several
test cases are proposed to validate these methods for the Modified Shallow
Water equations and the Two-Layer Shallow Water system.
