A well-balanced numerical model for depth-averaged two-layer shallow water flows

In this study, a well-balanced and positivity-preserving scheme for the nonconservative two-layer shallow water equations is developed in the framework of the path-conservative finite volume method. Special attention is paid to guaranteeing the well-balanced properties even in the presence of the wet–dry fronts for each layer. To this end, in this study, new numerical discretization and special local reconstruction are proposed. Moreover, the developed scheme also allows to stably compute flows in under-resolved meshes. The results of the numerical experiments illustrate the robustness and good performance of the constructed numerical scheme.