A model based on Hirano-Exner equations for two-dimensional transient flows over heterogeneous erodible beds

• The formulation of an appropriate and self-stable coupling of numerical schemes for two-dimensional transient flows over heterogeneous erodible beds.
• The numerical results are satisfactorily compared with 1D academic test cases and 2D experimental data. All of the cases studied are transient.
• It is shown that the adequate evaluation of the sediment transport fluxes for each fraction provide a correct estimation of the bed and surface texture, in terms of spatial and temporal evolution.

In order to study the morphological evolution of river beds composed of heterogeneous material, the interaction among the different grain sizes must be taken into account. In this paper, these equations are combined with the two-dimensional shallow water equations to describe the flow field. The resulting system of equations can be solved in two ways: (i) in a coupled way, solving flow and sediment equations simultaneously at a given time-step or (ii) in an uncoupled manner by first solving the flow field and using the magnitudes obtained at each time-step to update the channel morphology (bed and surface composition). The coupled strategy is preferable when dealing with strong and quick interactions between the flow field, the bed evolution and the different particle sizes present on the bed surface. A number of numerical difficulties arise from solving the fully coupled system of equations. These problems are reduced by means of a weakly-coupled strategy to numerically estimate the wave celerities containing the information of the bed and the grain sizes present on the bed. Hence, a two-dimensional numerical scheme able to simulate in a self-stable way the unsteady morphological evolution of channels formed by cohesionless grain size mixtures is presented. The coupling technique is simplified without decreasing the number of waves involved in the numerical scheme but by simplifying their definitions. The numerical results are satisfactorily tested with synthetic cases and against experimental data.