GALERKIN TECHNIQUE FOR WATER WAVE SCATTERING BY THIN VERTICAL *BARRIERS IN DEEP WATER

摘要

This paper is concerned with Galerkin technique employed to handle a class of classical water wave scattering problems involving a thin vertical barrier having four basic geometrical configurations present in infinitely deep water. For each of the barrier configurations, the problem has an exact solution which was obtained in the literature by employing various mathematical methods. Each method appears to be somewhat complicated. For each problem the reflection and transmission coefficients were obtained in closed form involving modified Bessel functions or computable definite integrals. In the present paper, all the four problems are reduced to first kind integral equations which, although were solved exactly earlier in the literature by employing some complicated methods, are solved here numerically employing the Galerkin approximation in terms of simple polynomials multiplied by appropriate weight functions whose forms are dictated by the physics of each problem. Very accurate numerical estimates for the reflection and transmission coefficients for each problem are then obtained utilizing the numerical solution of appropriate integral equation, and are depicted graphically against the wave number. The numerical results obtained by the present method coincide with those obtained earlier. The advantage of the present method is that it avoids the complicacy in obtaining the exact solution of the integral equations for each barrier configuration.