First Advisor

Scott A. Wells

Date of Award


Document Type


Degree Name

Master of Science (M.S.) in Civil & Environmental Engineering


Civil and Environmental Engineering




Hydrodynamics -- Mathematical models, Water quality -- Mathematical models




A three-dimensional numerical model was developed to simulate hydrodynamic, temperature, and water quality distributions in rivers and lakes. In an attempt to get rid of the extra approximation and complexity, no coordinate transformation has been done and z-coordinate system has been employed. The governing equations are the continuity equation, free surface equation, momentum equations, and conservation equations of temperature and water quality. The model employs the time splitting technique which allows splitting the directions in which we end with two-dimensional governing equations and eventually the solution ends with a tri-diagonal matrix, which is easily solved by Thomas algorithm. The first step after developing a numerical model and before adding more features or applying the model to a real case, the model should be verified. The verification of the model was done by implementing the model to known solutions test cases in additional to evaluating whether the code preserves fluid mass. A series of test cases is performed by comparing the model results with the analytical solutions as proposed by many modelers. The model showed good agreement between the analytical and the numerical solution.



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A research project report submitted in partial fulfillment of the requirement for the degree of Master of Science in Civil and Environmental Engineering.

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