Achieving accurate numerical results of hydrodynamic loads based on the potential-flow theory is very challenging for structures with sharp edges, due to the singular behavior of the local-flow velocities. In this paper, we introduce the Extended Finite Element Method (XFEM) to solve fluid-structure interaction problems involving sharp edges on structures. Four different FEM solvers, including conventional linear and quadratic FEMs as well as their corresponding XFEM versions with local enrichment by singular basis functions at sharp edges, are implemented and compared. To demonstrate the accuracy and efficiency of the XFEMs, a thin flat plate in an infinite fluid domain and a forced heaving rectangle at the free surface, both in two dimensions, will be studied. For the flat plate, the mesh convergence studies are carried out for both the velocity potential in the fluid domain and the added mass, and the XFEMs show apparent advantages thanks to their local enhancement at the sharp edges. Three different enrichment strategies are also compared, and suggestions will be made for the practical implementation of the XFEM. For the forced heaving rectangle, the linear and 2nd order mean wave loads are studied. Our results confirm the previous conclusion in the literature that it is not difficult for a conventional numerical model to obtain convergent results for added mass and damping coefficients. However, when the 2nd order mean wave loads requiring the computation of velocity components are calculated via direct pressure integration, it takes a tremendously large number of elements for the conventional FEMs to get convergent results. On the contrary, the numerical results of XFEMs converge rapidly even with very coarse meshes, especially for the quadratic XFEM.

中文翻译：

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通过扩展有限元方法 (XFEM) 对具有锐利边缘的结构进行准确有效的流体动力学分析：2D 研究

由于局部流速的奇异行为，基于势流理论获得准确的流体动力载荷数值结果对于具有尖锐边缘的结构来说非常具有挑战性。在本文中，我们介绍了扩展有限元方法 (XFEM) 来解决涉及结构锐边的流固耦合问题。实现并比较了四种不同的 FEM 求解器，包括传统的线性和二次 FEM 以及它们对应的 XFEM 版本，这些版本通过在尖锐边缘的奇异基函数进行局部丰富。为了证明 XFEM 的准确性和效率，我们将研究无限流体域中的薄平板和自由表面上的强制升沉矩形，这两个维度都是二维的。对于平板，对流体域中的速度势和附加质量都进行了网格收敛研究，由于 XFEM 在尖锐边缘处的局部增强，它们显示出明显的优势。还比较了三种不同的丰富策略，并对 XFEM 的实际实施提出建议。对于受迫垂荡矩形，研究了线性和二阶平均波浪载荷。我们的结果证实了之前文献中的结论，即传统的数值模型不难获得附加质量和阻尼系数的收敛结果。然而，当需要计算速度分量的二阶平均波浪载荷通过直接压力积分计算时，传统 FEM 需要大量元素才能获得收敛结果。相反，即使网格非常粗糙，XFEM 的数值结果也能快速收敛，尤其是二次 XFEM。