Diffusion–dispersion numerical discretization for solute transport in 2D transient shallow flows

The 2D solute transport equation can be incorporated into the 2D shallow water equations in order to solve both flow and solute interactions in a coupled system of equations. In order to solve this system, an explicit finite volume scheme based on Roe’s linearization is proposed. Moreover, it is feasible to decouple the solute transport equation from the hydrodynamic system in a conservative way. In this case, the advection part is solved in essence defining a numerical flux, allowing the use of higher order numerical schemes. However, the discretization of the diffusion–dispersion terms have to be carefully analysed. In particular, time-step restrictions linked to the nature of the solute equation itself as well as the numerical diffusion associated to the numerical scheme used are question of interest in this work. These improvements are tested in an analytical case as well as in a laboratory test case with a passive solute (fluorescein) released from a reservoir. Experimental measurements are compared against the numerical results obtained with the proposed model and a sensitivity analysis is carried out, confirming an agreement with the longitudinal coefficients and an underestimation of the transversal ones, respectively.