A general paradigm of modeling two-dimensional overland watershed water quality

This paper presents the development of sediment and reactive chemical transport in two-dimensional overland watershed systems. Through decomposition of reaction network via Gauss-Jordan column reduction: (a) redundant fast reactions and irrelevant kinetic reactions are removed from the system; (b) fast reactions and slow reactions are decoupled; and (c) species reaction equations are transformed into two sets: equilibrium species mass action equations and kinetic-variable reaction equations. This enables our model to include as many types of reactions as possible, choose kinetic-variables instead of chemical species as primary dependent variables, and simplify the reaction terms in transport equations. In our model, five options are provided to solve the advection-dispersion transport equation: finite element method in conservative form, finite element method in advective form. Lagrangian-Eulerian approach, Lagrangian-Eulerian approach with finite element method in conservative form for boundary, and Lagrangian-Eulerian approach with finite element method in advective form for boundary. The production-consumption rate of chemical species is determined by reaction-based formulations. To improve the efficiency and robustness of the computation, there are three options in the reactive chemical transport to deal with the reaction term: fully-implicit, mixed predictor-corrector and operator splitting, and operator splitting. One example problem is employed to demonstrate the design capability of the model and the robustness of the numerical simulations.