A well-balanced path conservative SPH scheme for nonconservative hyperbolic systems with applications to shallow water and multi-phase flows

Several test problems (both in 1D and 2D) are presented in the final part of the paper for different systems of non-conservative hyperbolic equations: the Baer Nunziato model of compressible multi-phase flows, the one- and two-layer shallow water equations and the Pitman & Le two-phase debris flow model. The numerical results for each system of equations have been compared with available reference solutions to verify the accuracy of the proposed scheme. For the shallow water type models under consideration the method proposed in this paper has furthermore been shown to be well-balanced up to machine precision.