Masters Theses

Date of Award

5-1990

Degree Type

Thesis

Degree Name

Master of Science

Major

Engineering Science

Major Professor

A. J. Baker

Committee Members

Osama Soliman, James A. Euler

Abstract

A pilot research code has been upgraded technically and aesthetically to a fully applied hydrodynamics package. This set of five programs, entitled FATHOM, approximately solves the two-dimensional free surface hydromechanics form of the Navier-Stokes equations. Included in the program set is an automated grid generator, the ability to define various types of flow obstructions, as well as access to a wide variety of graphical input/output devices. Flexibility, accuracy, ease of use and solution stability are documented with results from six test cases chosen to examine a wide and challenging variety of applications in free-surface hydrodynamics. This report constitutes a complete user's guide for the five program system FATHOM. The numerical approximation is implemented through a finite element spatial discretization. This yields a time dependent, first-order differential equation system. These ordinary differential equations are integrated through an implicit scheme of variable order. The finite element analysis is carried out utilizing Taylor weak statement theory to increase stability. The integration in time may be performed employing either a rectangular, trapezoidal or implicit Runge-Kutta scheme. A tensor matrix factorization allows the resulting matrix equation system to be solved economically. A range of benchmark problems are reported examining stability, accuracy, ease of use and flexibility. Results are presented confirming that these demands are met by FATHOM. Additionally, the implementation of the tensor matrix factorization effectively reduces the amount of computation execution time drastically over traditional direct methods.

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