A robust numerical model for shallow water governing solute transport with wet/dry interfaces

In this study, a robust numerical model is developed to guarantee that the C-property for both hydrodynamic and solute transport models and positivity of both water depth and solute concentration. Moreover, special attention is paid to satisfying such properties in the unstructured triangular cells near wet-dry interfaces. In the developed numerical model, the finite-volume central-upwind scheme is adopted to approximate the advective fluxes, and Green's theorem is applied to estimate the diffusive fluxes. The C-property for hydrodynamic model near wet-dry area is achieved by introducing an auxiliary free surface variable used in the piecewise linear reconstruction and discretizing the bed slope source term in a special form. And the C-property for solute transport is guaranteed by reconstructing secondary variables instead of the primary variables within the frame of central-upwind method, and using the coupling approach for the governing system. The positivity of the solute concentration is satisfied using a proposed diluting time step restriction and the positivity of the water depth is guaranteed by a draining time technique. The desired properties of the proposed numerical model are verified by several numerical experiments. (C) 2019 Elsevier B.Y. All rights reserved.