A new semi-Lagrangian routing procedure for constituent transport in steady and unsteady flow velocity fields

In this paper, a new numerical model for the simulation of constituent transport in both steady and unsteady flow conditions is presented. The transport model is a routing procedure in which the advection process is solved by means of the Lagrangian coordinate transformation, while the dispersion process is approximated within each time step by means of the convolution principle, exploiting a multilinear procedure. In order to facilitate the application of the Lagrangian coordinate transformation during unsteady flow conditions, the unsteady velocity field corresponding to the linearized parabolic approximation of the Saint Venant Equations is provided, taking into account appropriate boundary conditions. Finally, classic BOD-DO relationships are embedded into the routing procedure in order to perform water quality applications with reactive constituents. The model is first demonstrated with respect to a numerical water quality model in both steady and unsteady hydraulic conditions, and is then applied to two real-world cases. Because of its characteristics, the proposed model seems suitable for real time forecast of pollutant concentrations when an emergency event occurs, or for water quality management in real rivers.