Nation Taiwan Ocean University Department of Harbor and River June 25, 2015 pp.1 Null-field integral equation approach for the scattering water wave problems with circular boundaries 研 究 生 : 柯佳男 指導教授 : 陳正宗博士 日 期 : 2007/01/11

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.2 Outlines  Motivation and literature review  Mathematical formulation Expansions of fundamental solution and boundary density Adaptive observer system Vector decomposition technique Linear algebraic equation  Numerical examples Water wave problem with two circular cylinders  Conclusions

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.3 Outlines  Motivation and literature review  Mathematical formulation Expansions of fundamental solution and boundary density Adaptive observer system Vector decomposition technique Linear algebraic equation  Numerical examples Water wave problem with two circular cylinders  Conclusions

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.4 Motivation  In many of large ocean structures, the interaction between water waves and arrays of bodies has become increasingly important and work has been done on the subject in recent years.  Exact solutions are limited for the simple case. Numerical solutions are generally required in engineering application.  Subsequently, much of the work due to the scattering of water waves by arrays of bodies have already turned into interesting of evaluating wave forces.

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.5 Literature review  The null-field (or T-matrix) method Waterman, 1969 (single scatter) Peterson and Strom, 1979 (several scatters )  Wave forces on cylinder arrays McIver & Evans, 1984  Shallow water wave Mingde & Yu, 1987

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.6 Outlines  Motivation and literature review  Mathematical formulation Expansions of fundamental solution and boundary density Adaptive observer system Vector decomposition technique Linear algebraic equation  Numerical examples Water wave problem with two circular cylinders  Conclusions

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.7 Expansions of fundamental solution (2D)  Laplace problem--  Helmholtz problem-- O s x x

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.8 Boundary density discretization  Fourier series expansions - boundary density Fourier series Ex. constant element

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.9 Adaptive observer system Source point collocation point

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.10 Linear algebraic equation

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.11 Flowchart of present method Degenerate kernel Fourier series Null-field equation Algebraic system Fourier Coefficients Potential Analytical Numerical

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.12 Outlines  Motivation and literature review  Mathematical formulation Expansions of fundamental solution and boundary density Adaptive observer system Vector decomposition technique Linear algebraic equation  Numerical examples Water wave problem with two circular cylinders  Conclusions

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.13 Water wave (3-D) W-Wave

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.14 邊界條件 ( 運動自由表面邊界條件 ) ( 側面邊界條件 ) ( 底床邊界條件 ) ( 動力自由表面邊界條件 ) I. 合併 II. 滿足 可令

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.15 Governing equation Governing equation: (Laplace equation) (Helmholtz equation)

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.16 Water wave (2-D) W-Wave

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.17 Decomposition of coordinate Where:

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.18 Outlines  Motivation and literature review  Mathematical formulation Expansions of fundamental solution and boundary density Adaptive observer system Vector decomposition technique Linear algebraic equation  Numerical examples Water wave problem with two circular cylinders  Conclusions

Mechanics Sound Vibration Laboratory HRE. NTOU June 25, 2015 pp.19 Conclusions  We will calculate the water wave force by using the potential function  We will develop a set of formulation for arbitrary number of circular cylinders with arbitrary radii, proportion and location for the scattering water wave problems

Nation Taiwan Ocean University Department of Harbor and River June 25, 2015 pp.20 Thanks your kind attentions You can get more information on our website.