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研 究 生 : 柯佳男 指導教授 : 陳正宗博士 日 期 : 2007/01/11

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. Outlines. Motivation and literature review Mathematical formulation Expansions of fundamental solution and boundary density

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研 究 生 : 柯佳男 指導教授 : 陳正宗博士 日 期 : 2007/01/11

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  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

  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

  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

  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.

  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

  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

  7. Expansions of fundamental solution (2D) • Laplace problem-- • Helmholtz problem-- x x s O

  8. Boundary density discretization • Fourier series expansions - boundary density Fourier series Ex . constant element

  9. Adaptive observer system Source point collocation point

  10. Linear algebraic equation

  11. Degenerate kernel Fourier series Potential Null-field equation Algebraic system Fourier Coefficients Analytical Numerical Flowchart of present method

  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

  13. W-Wave Water wave (3-D)

  14. (動力自由表面邊界條件) (運動自由表面邊界條件) (側面邊界條件) (底床邊界條件) 邊界條件 I. 合併 可令 II. 滿足

  15. Governing equation Governing equation: (Laplace equation) (Helmholtz equation)

  16. W-Wave W-Wave Water wave (2-D)

  17. Where: Decomposition of coordinate

  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

  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

  20. Thanks your kind attentions You can get more information on our website. http://msvlab.hre.ntou.edu.tw/

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