| Modeling of naturally occurring hydraulic systems is primarily done using numerical approximations to the de Saint Venant series of equations. Numerical approximations to the de Saint Venant equations exist in one, two, and three dimensions (1D, 2D, 3D). As the dimensionality of the approximation increases, so does the complexity of the numerical method, requiring increased computational times. Many areas modeled have complex geometries not easily described by 1D approximations. However, in many cases, use of a fully 2D or 3D model is computationally wasteful, as the channels that exist within the solution grid can be computationally evaluated as 1D. The purpose of this thesis is to develop a linked 1D-2D model that proves advantageous over models that are either fully one or two-dimensional, while retaining the strengths of both. The development of the final model was accomplished after trying several different one and two-dimensional models and linking schemes. The models were first developed in one-dimension where they were tested for conservation and error convergence. The models were also tested for their ability to handle rapidly changing flow situations, such as those encountered by dam-break scenarios.;After development, the models were tested against flow situations where analytical solutions are known. The linking methodology was developed in order to maintain conservation across the link. The final product was found to be computationally faster than a full 2D model, while maintaining the information needed to accurately predict flow characteristics within large bays or reservoirs. Additionally, the method is simple to manipulate; adding 1D or 2D components is simple and can take place in any computationally viable orientation. |
