Dual boundary element method for determining the reflection and transmission coefficient of oblique incident wave passing a thin submerged breakwater

Abstract

In this paper, the dual integral formulation for the modified Helmholtz equation in solving the propagation of oblique incident wave passing a thin barrier (a degenerate boundary) is derived. All the improper integrals for the kernel functions in the dual integral equations are reformulated into regular integrals by integrating by parts and are calculated by means of the Gaussian quadrature rule. The jump properties for the single layer potential, double layer potential and their directional derivatives are examined and the potential distributions are shown. To demonstrate the validity of the present formulation, the transmission and reflection coefficients of oblique incident wave passing a thin rigid barrier are determined by the developed dual BEM program. Also, the results are obtained for the case of wave scattering by a rigid barrier with a zero thickness in a constant wate depth and are compared with those of experiment and analytical solution using eigenfunction expansion method. Good agreement is made.本文以對偶邊界元素法(DBEM)分析潛堤承受斜向與正向入射波所造成的消波影響。於分析時，將奇異積分方程(UT式)及超奇異積分方程(LM式)之奇異積分轉換成正規積分。並分析單層勢能與其方向導微之勢能的跳躍行為，而繪出其勢能分布圖，進而發展一套解斜向與正向入射問題的對偶邊界元素程式。藉由此程式可得知流場的變化，計算出反射係數、穿透係數。於極薄潛退化邊界問題時，將UT式及LM式的相依方程組的互換，解決解不唯一的問題。最後並以實例比較本法、解析解、有限元素法與實驗所得的數值結果，驗證本法的可行性。