Modelling suspended load with moment equations and linear concentration profiles

In numerical simulations, it is always necessary to find an optimum between the simplicity of the model and a good representation of real phenomena. In the field of hydraulic flows simulations, the models using depth-averaged and moment equations are an interesting compromise between full 3D and simple depth-averaged models. This paper presents the use of a moment equation for suspended load transport. A simple but representative model for the sediment concentration profiles is developed. This original bi-linear concentration profile is compared to the traditional Rouse-profiles and shows a good correspondence despite its great simplicity. Advective and diffusive sediment fluxes are developed analytically and lead to a concise formulation, which is an asset for practical use. A differential equation for the sediment concentration moment is also fully developed, and a special attention is cast to the source term. The finite volume scheme has been chosen to implement the model, because it is particularly well suited for highly advective transport equations, it is conservative and it makes the choice of the upwinding easier. 1D simulations show the capacity of the model to reproduce laboratory experiments described in the literature.