Numerical Solution of the Nonlinear Ship Wave Problem (Computational Methods)
Chamberlain, Robert Rexford, Jr.
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Permalink
https://hdl.handle.net/2142/70627
Description
Title
Numerical Solution of the Nonlinear Ship Wave Problem (Computational Methods)
Author(s)
Chamberlain, Robert Rexford, Jr.
Issue Date
1984
Department of Study
Aeronautical and Astronautical Engineering
Discipline
Aeronautical and Astronautical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Aerospace
Abstract
This thesis is a systematic development of a general numerical method for the solution of the nonlinear ship wave problem. Analytical approaches to this problem must always be linearized and are often unable to handle arbitrary and complicated hull geometry in the presence of a free surface. Other numerical approaches often provide inconsistent results for the physical quantities of interest, particularly the wave resistance. The present work unifies the numerical approach to the ship wave problem and considers all of the major aspects of the numerical method. Many of the features of the method are novel in the sense that they do not agree with the presently accepted views of the numerical ship hydrodynamics community.
The solution method is a time dependent finite difference technique which couples the time advancement of the free surface boundary conditions to a fast direct solution of the Laplace equation for the interior flow. The direct solver is optimized in the sense that the numerical solution in the entire domain need not be calculated or stored. A new type of mesh system is also developed so as to accurately accommodate the exact hull geometry, and the fast Laplace solver is modified by the capacitance matrix technique in order to implement the hull boundary condition. Furthermore, it is found that by increasing the size of the computational region so that the downstream boundary is far from the ship, an effective open boundary condition which is far simpler than what has been proposed in the past may be implemented.
Results are obtained for the thin ship and Neumann-Kelvin problems and are compared to existing solutions and to experiments. It is generally found that the linearized, inviscid models presently in use are unable to adequately predict in a quantitative way the extremely small values of wave resistance over a wide range of Froude numbers. It is therefore shown in detail how the numerical groundwork developed in this thesis may be extended to solve the full nonlinear ship wave problem.
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