High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems in (Parés, SIAM J. Numer. Anal. 44:300–321, 2006; Castro et al., Math. Comput. 75:1103–1134, 2006; J. Sci. Comput. 39:67–114, 2009). Recently, it has been observed in (Abgrall and Karni, J. Comput. Phys. 229:2759– 2763, 2010) that this approach may have some computational issues and shortcomi...
