本文針對橢圓型態之緩坡方程式，以有限元素法建立波浪數值模式，模式中考量波浪於近岸傳遞時可能因地形及結構物產生能量消散等變化，擬將模式延伸至包含非線性淺化、碎波及潛式透水結構物等範疇。模式建立時所採用之邊界條件為近似輻射邊界條件，而外海開放邊界條不等水深處，則是沿用許等人 (2001) 所提出之不等水深輻射邊界條件予以設定。文中主要探討各碎波指標及碎波能量消散項應用於模式之適用性，並進一步加入非線性淺化修正項以改善線性淺化公式於描述波浪碎波波高之不足。此外，考慮實際應用時可能面臨之潛式透水結構物問題，於緩坡方程式中加入透水介質效應以期能反應出波浪於透水結構物中能量之損失效應。經由波浪通過各式斜坡底床地形的校核計算，結果經與實驗數據之比較顯示應用McCowan (1894) 及Dally等人 (1985) 之碎波指標及碎波能量消散公式模擬波浪於斜坡上碎波所獲結果較為滿意，而非線性淺化修正項亦提升能模式預測碎波點附近波高之精確性。此外，對於波浪通過透水潛堤之測試中，顯示考慮透水效應之波場模式可以得到與實驗數據相近之計算結果。

A numerical model based on elliptic mild–slope equation is developed using finite element method. The model is extended to include the effects of wave breaking, nonlinear shoaling and waves propagating over a submerged permeable breakwater. The radiation boundary condition is approximated to the second-order term for wave with large angle incidence. On the open boundaries with varying depth, the boundary conditions proposed by Hsu et al. (2001) is adopted. To verify the validity of the present model, cases of wave propagating over different sloping beaches were run using the developed computer program. The results show that the wave criteria addressed by McCowan (1894) and by Dally et al. (1985) provide more accurate predictions in the numerical calculation. Furthermore, numerical results also show that the addition of nonlinear shoaling term in the mild-slope equation could improve underestimation of wave height around the breaking point. The model is also examined for the cases of waves passing over submerged permeable breakwaters. Model results are well compared with the experimental data.

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