本文是利用邊界元素法港池振盪數值模式來計算，希望了解入射波浪進入已知港池後，港池內外波浪分佈的情形。本文的目的主要是希望將原本一階港池振盪計算，運用二階的邊界條件，令其計算在二階上，以期能夠更準確的模擬非線性之波浪對港池振盪之影響。
先將波浪場利用勢能波浪理論描述，所求解之非線性問題則利用泰勒級數展開，配合攝動法將問題表示成第一階和第二階邊界值問題，先將二階解分為水面非齊性通解與特解，通解部分為直接利用類似一階的港池振盪模式，代入二階條件計算，然後特解部份則是利用邊界元素法港池振盪數值模式所得出之一階振幅之值，將其轉換並代入第二階邊界值問題，藉以得到二階港池振盪問題之解，所求得之解，在與前人所作之研究比較上，有相當的準確度。

The purpose of this thesis is to calculate the problem of harbor resonance using a boundary element method. The nonlinear problems are considered, and calculated up to the second-order. In the numerical calculation, the first-order problem is simulated using the well known computational scheme originally proposed by Lee (1969). The second-order problem is separated into two parts, one with homogeneous free surface boundary condition, and the other with nonhomogeneous free surface condition. The second-order homogeneous problem is similar to the first-order problem, and is solved following the first-order procedure, except using the second-order wave number and the corresponding second-order incident wave condition. As for the nonhomogeneous problem, it is solved semi-analytically using the first-order numerical solutions. The present numerical model is used to investigate the second-order characteristics of the harbor resonant problem. The results indicate that the second-order consideration tends to increase the response wave energy inside the harbor basin, and should be important to be considered in harbor engineering.

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