A conservative, semi-Lagrangian fate and transport model for fluvial systems—I. Theoretical development

In this paper a new conservative, semi-Lagrangian fate and transport model for fluvial systems is presented. Following an outline of the current trends in water quality modelling, the main features of Eulerian and semi-Lagrangian modelling approaches are discussed. It is argued that an inherently conservative semi-Lagrangian approach offers a way of meeting the future needs of the industry. The semi-Lagrangian philosophy for advection is then outlined and further developed with the authors explaining how dispersive transport, simple first-order decay terms and inflow boundary conditions can be incorporated within the algorithm. The method (termed DISCUS) possesses high accuracy but, in contrast to other semi-Lagrangian fluvial transport codes, it is centred around a finite-volume based mass balance, which guarantees mass conservation and makes it amenable to flux limiting techniques for suppressing non-physical grid-scale oscillations. The method’s semi-Lagrangian character allows it to work at very large time steps, which makes it efficient for long-term and multiple scenario simulations. The method’s robustness and inherent stability make it particularly useful for highly non-uniform streams and variable loading conditions and also for complex interacting chemical species.