A novel well-balanced numerical model for water-solute mixture underflows coupled with ambient water

This study considers a water-solute mixture underflow coupled with ambient water. Such physical phenomenons are modelled by a two-layer stratified Saint-Venant system with a scalar transport equation in this paper. The governing system is first relaxed to a hyperbolic system discretized by a path-conservative algorithm. In such framework, a novel discrete formula of nonconservative and source terms, is proposed to be able to guarantee the well-balanced property for the hydrodynamic model and preserve the uniform concentration in underflows, especially at wet-dry fronts. The performances of the developed numerical schemes are verified by several tests.