A structure-preserving nonstaggered central scheme for shallow water equations with wet–dry fronts and Coriolis force on triangles

Abstract

This work introduces a structure-preserving nonstaggered central scheme for the two-dimensional shallow water equations with wet–dry fronts and Coriolis force on triangular meshes. A key innovation of our approach is the development of a novel discretization method for source terms that exploits the geometric properties of the mesh within staggered cells. This method effectively overcomes the limitations of existing central schemes, which often exhibit a lack of well-balanced property in configurations that involve wet–dry fronts. In particular, the defined numerical fluxes not only utilize information from the central points but also from the vertex points. We rigorously show that the proposed numerical scheme maintains both positivity-preserving and well-balanced properties, essential attributes that ensure the physical validity and stability of the simulations. To verify our theoretical results, we conduct comprehensive numerical experiments that encompass a variety of scenarios. The results highlight the method’s exceptional performance in accurately modeling complex fluid dynamics associated with wet–dry fronts and Coriolis force.