A reaction-based river/stream water quality model: Model development and numerical schemes

SummaryThis paper presents the conceptual and mathematical development of a numerical model of sediment and reactive chemical transport in rivers and streams. The distribution of mobile suspended sediments and immobile bed sediments is controlled by hydrologic transport as well as erosion and deposition processes. The fate and transport of water quality constituents involving a variety of chemical and physical processes is mathematically described by a system of reaction equations for immobile constituents and advective–dispersive–reactive transport equations for mobile constituents. To circumvent stiffness associated with equilibrium reactions, matrix decomposition is performed via Gauss–Jordan column reduction. After matrix decomposition, the system of water quality constituent reactive transport equations is transformed into a set of thermodynamic equations representing equilibrium reactions and a set of transport equations involving no equilibrium reactions. The decoupling of equilibrium and kinetic reactions enables robust numerical integration of the partial differential equations (PDEs) for non-equilibrium-variables. Solving non-equilibrium-variable transport equations instead of individual water quality constituent transport equations also reduces the number of PDEs. A variety of numerical methods are investigated for solving the mixed differential and algebraic equations. Two verification examples are compared with analytical solutions to demonstrate the correctness of the code and to illustrate the importance of employing application-dependent numerical methods to solve specific problems.