Analytical and field verification of a 3D hydrodynamic and water quality numerical scheme based on the 2D formulation in CE-QUAL-W2

Abstract

A new 3D hydrodynamic model was developed to simulate water quality transport in surface waterbodies. The governing equations are the continuity equation, free surface equation, momentum equation, and transport equation. The 2D numerical scheme of CE-QUAL-W2 was expanded in three dimensions and modified to solve for the free surface elevation. A time splitting technique was employed to solve the momentum and transport equation. The numerical formulation of the 3D scheme used a novel solution, which resulted in a tri-diagonal matrix form for solving the free surface equation rather than a more computationally intensive penta-diagonal matrix solution. In addition, the hydrodynamic and water quality equations were solved at the same time step in order to allow feedback between water quality and hydrodynamics. The verification of the model hydrodynamics and temperature was performed by comparing the model predictions to known analytical solutions and field data from Lake Chaplain, Washington, USA. There was good agreement of the solution of the hydrodynamic equations to analytical solutions and field data.

A Unique Volume Balance Approach for Verifying the Three-Dimensional Hydrodynamic Numerical Models in Surface Waterbody Simulation

“…To implement the volume balance approach, the three-dimensional model W3 developed by [13] for modeling hydrodynamics, temperature, and water quality in surface waterbodies was employed. Using the finite differences, the model solves the governing equations of continuity, free surface, momentums, and mass transport.…”

“…Using the finite differences, the model solves the governing equations of continuity, free surface, momentums, and mass transport. Comparisons with analytical solutions and field data were carried out for verifying and validating the W3 model [13][14][15][16][17].…”

Modeling Thermal Stratification Effects in Lakes and Reservoirs

“…One reason may be that the data and parameter uncertainty increase in higher dimensional models [34]. In a comparison of 2D and 3D models, many examples have shown [28,35,36] that 2D models often better represent temperature profiles than some 3D models. There may be many reasons for this, but the important message is that more complicated models do not necessarily mean better model predictions.…”