修正型缓坡方程的有限元模型

发布时间：2018-07-09 17:39

  本文选题：修正型缓坡方程 + 有限元　； 参考：《海洋学报》2017年01期

【摘要】：与缓坡方程相比,修正型缓坡方程增加了地形曲率项和坡度平方项,从而提高了数值求解的复杂性。本文将计算域划分为内域和外域,内域为水深变化区域,使用修正型缓坡方程,其中的地形曲率项和坡度平方项可用有限单元各节点的水深信息和单元插值函数表示,外域为水深恒定区,速度势满足Helmholtz方程,通过内外域的边界匹配建立有限元方程,并用高斯消去法求解。进而分别模拟了波浪传过Homma岛和圆形浅滩的变形,其结果与相关的解析解和实验数据吻合良好,证明了本文有限元模型的正确性。同时,通过与实验数据的对比也明显看出,在地形坡度较陡的情况下,修正型缓坡方程较缓坡方程具有更高的计算精度。
[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.
【作者单位】： 大连理工大学海岸和近海工程国家重点实验室;浙江海洋大学港航与交通运输工程学院;
【基金】：国家自然科学基金(51379032,51490672)
【分类号】：P731.22
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本文编号：2110121