Using Modified Finite Point Method to Simulate Harbor Resonance induced by Water Waves
Date Issued
2012
Date
2012
Author(s)
Chiang, Kuo-Cheng
Abstract
The objective of this study focuses on extending the modified finite point mesh-less numerical model to the analysis of the harbor resonance induced by water waves. Harbor resonance is a phenomenon caused by ocean waves intruding into the harbor on coastal areas. When it occurs, it would seriously affect the safety of the ships in the harbor. Therefore, analysis of harbor resonance is an important matter in the process of harbor planning and design. The purpose of this study is to verify present model’s accuracy and applicability by comparing with available analytical solutions. Present numerical model after verifications can apply to harbor engineering practices.
In this study, the governing equation is the mild-slop equation. It can be simplified to the Helmholtz equation when water depths remain constant in the computational domain. A special mesh-less numerical methods, namely, modified finite point method (MFPM) (Wu & Tsay, 2011) is employed in present study. Based on collocation, this method uses polynomials as the local solution form needed in the collocation approach. In previously research, it has been shown that MFPM can efficiently calculate the solutions and the partial derivatives of the unknown function. When breakwaters appear in the computational domain, a concept of subdomains is designed to obtained accurate solutions. Present mesh-less numerical method is easy to generate computational points, especially in irregular regions.
To verify accuracy of present numerical model, examples of three types of harbors, with or without breakwaters, are calculated to obtain amplification factor at a specific point for different parameters, which are products of incident wave numbers and radius of circular harbor or length of a rectangular one. Present numerical results are compared with the analytical solutions by Mei and Petroni(1973),. Very good agreements are observed. Two-dimensional contours of wave amplitude and graphs of velocity vectors are demonstrated in these examples.
Subjects
harbor resonance
mild-slope equation
mesh-less method
modified finite point method
local polynomial approximation
amplification factor
Type
thesis
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