A robust coupled model for solute transport driven by severe flow conditions

This paper introduces a computationally efficient model that solves a 4 × 4 matrix form of the hyperbolic conservation laws consisting of the 2D shallow water and advection-diffusion equations. The model allows automatic shock-capturing due to the implementation of a finite volume Godunov-type scheme featured with an HLLC approximate Riemann solver. The numerical scheme is also able to provide well-balanced solutions and maintain non-negative water depth and solute concentration for applications involving wetting and drying over complex domain topographies. Implemented on a simplified adaptive grid system, the model can save 3-17 times of computational cost without compromising solution accuracy for those simulations with predominant localised complex hydrodynamic or flow features, as demonstrated by the numerical experiments. Therefore, the current model provides a potential tool for efficient simulation of large-scale solute transport as well as flow hydrodynamics during a highly transient flood event caused by dam failure or flash flooding.