本文選題：修正型緩坡方程 + 有限元��； 參考：《海洋學(xué)報(bào)》2017年01期

【摘要】：與緩坡方程相比,修正型緩坡方程增加了地形曲率項(xiàng)和坡度平方項(xiàng),從而提高了數(shù)值求解的復(fù)雜性。本文將計(jì)算域劃分為內(nèi)域和外域,內(nèi)域?yàn)樗钭兓瘏^(qū)域,使用修正型緩坡方程,其中的地形曲率項(xiàng)和坡度平方項(xiàng)可用有限單元各節(jié)點(diǎn)的水深信息和單元插值函數(shù)表示,外域?yàn)樗詈愣▍^(qū),速度勢(shì)滿足Helmholtz方程,通過內(nèi)外域的邊界匹配建立有限元方程,并用高斯消去法求解。進(jìn)而分別模擬了波浪傳過Homma島和圓形淺灘的變形,其結(jié)果與相關(guān)的解析解和實(shí)驗(yàn)數(shù)據(jù)吻合良好,證明了本文有限元模型的正確性。同時(shí),通過與實(shí)驗(yàn)數(shù)據(jù)的對(duì)比也明顯看出,在地形坡度較陡的情況下,修正型緩坡方程較緩坡方程具有更高的計(jì)算精度。
[Abstract]:Compared with the gentle slope equation, the modified gentle slope equation increases the topographic curvature term and the square term of the slope, thus improving the complexity of the numerical solution. In this paper, the computational domain is divided into inner and outer regions, the inner region is the region of water depth, the modified gentle slope equation is used, and the topographic rate term and the square term of the slope can be used in the finite element nodes. The water depth information and the element interpolation function indicate that the outer region is a constant area of water depth, the velocity potential satisfies the Helmholtz equation, the finite element equation is established through the boundary matching between the inner and outer regions, and the Gauss elimination method is used to simulate the deformation of the waves passing through the Homma island and the circular shoal respectively. The results are in good agreement with the relevant analytical solutions and the experimental data. It is proved that the finite element model of this paper is correct. At the same time, by comparing with the experimental data, it is obvious that the modified gentle slope equation has a higher calculation precision than the gentle slope equation in the case of the steep terrain slope.
【作者單位】： 大連理工大學(xué)海岸和近海工程國家重點(diǎn)實(shí)驗(yàn)室;浙江海洋大學(xué)港航與交通運(yùn)輸工程學(xué)院;
【基金】：國家自然科學(xué)基金(51379032,51490672)
【分類號(hào)】：P731.22
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本文編號(hào)：2110121