1. Wave propagation through arrays of unevenly spaced vertical piles Adviser ： Jeng-Tzong Chen Date: February 06, 2009 Place: HR2 307 Reporter : Yi-Jhou Lin National Taiwan Ocean University Department of Harbor and River Engineering

2. 2 Outlines Problem statement Numerical examples Concluding remarks

3. 3 Problem statement Governing equation: Separation variable : where Seabed boundary conditions : Original Problem Free-surface conditions :

4. 4 Decompose two parts ＝ Radiation field (typical BVP) Free field Original Problem ＋

5. 5 Flowchart Original problem Decompose two parts Free fieldRadiation field Expansion Fourier series of boundary densities Degenerate kemel For fundamental solution Collocate of the real boundary Linear algebraic system Calculation of the unknown Fourier BIE for the domain point Superposing the solution of two parts Total field

6. 6 Numerical examples Original Problem

7. 7 Near-traped mode (Duclos and Clement, 2004)

8. 8 Near-traped mode (Present, 2009)

9. 9 Perturbation parameter

10. 10 Perturbation parameter No trapped mode is found

11. 11 Horizontal force versus wave number

12. 12 Concluding remarks A general-purpose program for solving the water wave problems with arbitrary number, size and various locations of circular cylinders was developed. We have proposed a BIEM formulation by using degenerate kernels, null-field integral equation and Fourier series in companion with adaptive observer system. Near trapped mode is observed in this study.

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