A conservative, semi-Lagrangian fate and transport model for fluvial systems—II. numerical testing and practical applications

Abstract

In this paper a semi-Lagrangian fate and transport model for fluvial systems (DISCUS) is tested against exact solutions and against field data. Benchmark comparisons with an exact solution for the uniform advection–dispersion–decay equation (single reacting species) show that DISCUS possesses excellent accuracy characteristics over a wide range of time step sizes with accuracy usually highest at Courant numbers in excess of unity. In addition it is shown that numerical accuracy can be improved solely by increasing the time step. This is a tremendously useful trait of the model since numerical accuracy can be improved using reduced computational resources. The model is then tested against an exact solution for a multiple reacting species problem, namely computing the dissolved oxygen response of a uniform river to a periodic bio-chemical oxygen demand. Accuracy is again maintained at large time steps: indeed the error remains below 5% until the time step reaches the order of half the time period of the loading. Next the method is tested for two real-world water quality modelling situations. Firstly it is used to simulate a tracer experiment conducted over a non-uniform reach of the River Rhine in Germany. This shows the method’s ability to handle non-uniform rivers and inflow boundary conditions. DISCUS is shown to provide a high degree of accuracy at a small fraction of the computational cost of an explicit Eulerian method. Secondly, the model is tested against a pulse loading problem for multiple interacting species. A spill of milk (providing a bio-chemical oxygen demand) in a river in New Zealand provides the test case. This shows the potential of DISCUS for dealing with a variety of transformation terms, in this case by allowing the introduction of more complicated source and sink terms necessary to simulate the anoxic conditions that developed during the event. The model produces results of equal accuracy whether small or large time steps are used.