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An implicit method for water wave problems




Aston, Martha B., author
Thomas, J. W. (James William), 1941-, advisor
Zachmann, David W., committee member
Schubert, Wayne H., committee member

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This paper presents an implicit scheme for numerically simulating fluid flow in the presence of a free surface. The scheme couples numerical generation of a boundary-fitted coordinate system with an efficient solution of the finite difference equations. The method solves the two dimensional Navier-Stokes equations by applying an implicit backward in time difference scheme which is linearized by Taylor series expansion about the known time level to produce a system of linear difference equations. The difference equations are solved by an Alternating-Direction-Implicit procedure which defines a sequence of one dimensional block tridiagonal matrix equations. A standard block elimination scheme solves the one dimensional equations. For each time step, solutions for all equations are calculated simultaneously and noniteratively. Preliminary solutions of free surface fluid flow in an open channel are presented. These solutions are examined to define initial stability criteria for the numerical scheme.


1983 Spring.
Includes bibliographical references.

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Fluid dynamics -- Mathematical models
Waves -- Mathematical models
Differential equations, Linear


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