An Integrated Model of Hydrodynamics and Water Quality Transport

This paper presents the development of a numerical model to simulate integrated hydrodynamics and water quality transport in surface waters. The hydrodynamic module solves three-dimensional Navier-Stokes equations with or without the hydrostatic assumptions, and energy and salinity transport equations. The turbulence is modeled with generalized k-Ψ transport equations. The moving free surface is explicitly handled by solving the kinematic boundary condition equation using a node-repositioning algorithm. The water quality module solves sediment and reactive biogeochemical transport equations. The set of species transport equations were transformed into three subsets using a general paradigm of diagonalization. The first subset is made of transport equations of kinetic variables for slow/kinetic reactions. The second subset composes transport equations of components for reaction invariance. The third subset consists of transport equations of equilibrium variables, which can be used for posterior calculations of reaction rates of fast/equilibrium reactions. A set of nonlinear algebraic equations based on thermodynamic approaches is employed to close the system. The Arbitrary Lagrangian-Eulerian (ALE) representation is adopted for all transport equations. To provide robust, accurate, and efficient simulations, a variety of numerical schemes are provided. These include finite element methods or a combination of finite element and Semi-Lagrangian (particle tracking) methods. The model was applied to the Loxahatchee Estuary river system. The computational domain includes Loxahatchee estuary, Intracoastal Waterways, and three major tributaries of the river — the South Fork, North Fork, and Northwest Fork. Tides, currents, and salinity that are needed for water quality simulations were obtained from the hydrodynamics module of the integrated model. To demonstrate the flexibility and generality of water quality transport module, three widely used water quality models, WASP5, QUAL2E, and CE-QUAL-ICM, can be recast in the mode of reaction networks. Applications of WASP5 to the Loxahatchee estuary system using the model illustrated that it was treated simply as one example in light of the general paradigm of modeling reactive biogeochemical transport.