以雙互換邊界元素法求解修正型緩坡方程式

A Numerical Solution of Modified Mild-Slope Equation Using Dual Reciprocity Boundary Element Method

蕭松山(Sung-Shan Hsiao) ； 張君名(Chun-Ming Chang) ； 溫志中(Chih-Chung Wen)

《海洋工程學刊》 10卷1期 (2010/06) Pp. 65-86

https://doi.org/10.6266/JCOE.2010.1001.04

摘要

本文以修正型緩坡方程式(MMSE)爲解析波浪折、繞射以及反射共同效應之控制方程式，爲避免求解邊界積分方程式過程中所遭遇的複雜領域積分，應用雙互換邊界元素法(Dual Reciprocity Boundary Element Method, DRBEM)進行求解。數值計算例分別爲Homma圓島與沒水圓形淺灘，並且與Homma圓島之淺水長波解析解、沒水圓形淺灘之實驗值分別進行比較。由於在長波條件下MMSE之底床延伸項較不顯著，因此本文以720 sec 爲入射波週期進行計算，DRBEM-MMSE數值結果與解析解之結果十分吻合。此外，與沒水圓形淺灘實驗值比較結果，顯示DRBEM-MMSE之波浪模式有良好之準確度，對於圓形淺灘後方之計算準確度亦有顯著提升。本文成功的應用雙互換邊界元素法求解修正型緩坡方程式，且由於考量底床延伸項的關係顯著改善DRBEM-MSE之計算準確度。

關鍵字

雙互換邊界元素法 ； 修正型緩坡方程式 ； Homma 圓島 ； 沒水圓形淺灘

並列摘要

In this investigation, the modified mild-slope equation was solved by using dual reciprocity boundary element method (DRBEM) in order to avoid the corresponding domain integration due to non-homogenous terms of the wave governing equation. The numerical results of Homma's island and circular submerged shoal cases were compared with the analytic and numerical solutions and experiment results, respectively. In order to compare the numerical results of modified mild-slope equation with the analytic solutions of conventional mild-slope equation, the numerical experiments of wave period 720 sec were conducted in the limitation of long wave condition due to the lightly effect of bottom slope-square and curvature terms. Both of the numerical results of DRBEM-MSE and DRBEM-MMSE are in good agreement with analytic solution of the conventional MSE. Furthermore, the comparisons between the numerical and experiment results indicate that the results of DRBEM-MMSE can obtain the more accurate results than those of DRBEM-MSE. Finally, we can conclude that the DRBEM can be applied to solve the MMSE successfully and DRBEM-MMSE get more accurate results due to taking the bottom extended terms into account.

並列關鍵字

dual reciprocity boundary element method ； modified mild-slope equation ； Homma's island ； circular submerged shoal