“…In recent years, numerical methods for solving two-layer equations have received great attention and have been an object of intense research (Castro et al, 2001Kurganov and Petrova, 2009;Castro et al, 2010;Bouchut and Zeitlin, 2010;Fernández-Nieto et al, 2011;Canestrelli and Toro, 2012). A number of authors have presented different numerical schemes for non-conservative hyperbolic systems based on the finite-difference method (Fjordholm, 2012;Liu et al, 2015), finite-element method (Ljubenkov, 2015) or, more often, finite-volume method (FVM) (Castro et al, 2001;Kurganov and Petrova, 2009;Bouchut and Zeitlin, 2010;Canestrelli and Toro, 2012).…”