We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that
the scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied
to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its
high resolution and robustness in a number of numerical examples.