摘要
本研究採用基於平滑粒子流體動力學(SPH)方法的DualSPHysics數值模擬工具，對孤立波在斜坡上的溯升情形進行模擬與分析。首先，建立孤立波溯升的數值模型，模擬Synolakis (1987)孤立波於斜坡上溯升的實驗，包含不同水深及波高條件下之孤立波溯升，以及2種波高水深比(H/d)之孤立波溯升驗證，將數值模擬結果與Synolakis (1987)實驗資料進行比較，驗證DualSPHysics對孤立波溯升模擬擁有良好的可行性與準確性。接著，模擬Hsiao and Lin (2010)孤立波於梯形結構斜坡傳播的情形，將數值模擬結果與實驗值進行比較。 延伸Chergui and Bouzit (2022) 針對孤立波於階梯斜坡溯升問題的研究，本文探討不同階梯高度及斜坡條件對於孤立波溯升的影響，設計矩形、圓形及三角形三種階梯幾何形狀，分析各幾何形狀對孤立波溯升的影響。結果顯示，階梯高度與幾何形狀對孤立波溯升具有顯著影響。隨著階梯高度增加，孤立波的相對溯升高度降低，達到最大溯升高度的時間縮短，且最大溯升位置距堤趾的水平距離減少，顯示波浪達到最大溯升時更能遠離陸地。整體而言，三角形階梯在縮短最大溯升時間方面表現最佳，矩形階梯次之，而圓形階梯相對較差。此外，矩形階梯在減少最大溯升位置距堤趾水平距離更顯著，而圓形階梯則在較緩坡斜率1：20的條件下，對減小最大溯升位置距堤趾水平距離的效果更為明顯。 本研究驗證DualSPHysics模擬孤立波溯升的能力，並針對數值模擬過程中可能出現的問題進行討論，總結執行模擬時需要注意的事項。另外，根據模擬結果分析不同幾何形狀的階梯式斜坡對波浪溯升的影響，為相關研究提供參考依據。
並列摘要
In this study, the DualSPHysics numerical simulation tool based on the smoothed particle hydrodynamics (SPH) method is used to simulate and analyze the rise of solitary waves on a slope. Firstly, a numerical model of solitary wave runup is established to simulate the experiment of solitary wave runup on a slope by Synolakis (1987), including the runup of solitary waves under different water depths and wave heights, and the comparison between two wave height to water depth ratios (H/d). Solitary wave runup validation, comparing the numerical simulation results with the experimental data of Synolakis (1987), verifies that DualSPHysics has good feasibility and accuracy for solitary wave runup simulation. Next, the propagation of solitary waves on a trapezoidal structure slope in Hsiao and Lin (2010) is simulated and the numerical simulation results are compared with the experimental values. Extending the study of Chergui and Bouzit (2022) on the rise of solitary waves on stepped slopes, this paper investigates the effects of different step heights and slope conditions on the runup of solitary waves. Three step geometries, rectangular, circular, and triangular, are designed and analyzed. The effect of geometry on the runup of solitary waves. The results show that the step height and geometry have a significant effect on the solitary wave runup. As the step height increases, the relative runup height of the solitary wave decreases, the time to reach the maximum runup height is shortened, and the horizontal distance between the maximum runup position and the toe of the embankment decreases, indicating that the wave can move further away from the land when it reaches the maximum runup. Overall, the triangular steps perform best in shortening the maximum tracing time, followed by the rectangular steps, while the circular steps are relatively poor. In addition, the rectangular steps are more effective in reducing the horizontal distance between the maximum runup position and the dike toe, while the circular steps are more effective in reducing the horizontal distance between the maximum runup position and the dike toe under the condition of a gentle slope of 1:20. This study verifies the ability of DualSPHysics to simulate solitary wave runup, discusses the problems that may arise during the numerical simulation process, and summarizes the matters that need to be paid attention to when performing the simulation. In addition, the influence of stepped slopes with different geometric shapes on wave runup is analyzed based on the simulation results, providing a reference for related research.