用扩展有限元法（XFEM）精确有效地分析具有锐边结构的流体动力学：二维研究
Accurate and efficient hydrodynamic analysis of structures with sharp edges by the Extended Finite Element Method (XFEM): 2D studies
摘要：
由于局部流速的奇异性，对于具有锐边的结构，基于势流理论获得精确的水动力载荷数值结果是非常具有挑战性的。本文将扩展有限元法引入到求解尖边结构的流固耦合问题中。四种不同的有限元求解器，包括传统的线性和二次有限元以及相应的XFEM版本与局部富集的奇异基函数在尖锐的边缘，实现和比较。为了证明XFEM的精度和效率，将研究无限流体域中的薄平板和自由表面处的受迫起伏矩形，两者都是二维的。对于平板，网格收敛的研究进行了在流体域的速度势和附加质量，和XFEM显示出明显的优势，由于其在尖锐的边缘的局部增强。三种不同的富集策略也进行了比较，并提出建议，为实际实施的XFEM。对于强迫垂荡矩形，研究了线性和二阶平均波浪载荷。我们的结果证实了文献中的结论，这是不难为传统的数值模型，以获得收敛的结果，附加质量和阻尼系数。然而，当通过直接压力积分计算需要计算速度分量的二阶平均波浪载荷时，常规有限元法需要大量的单元才能得到收敛结果。与此相反，XFEM的数值结果收敛迅速，即使在很粗的网格，特别是对于二次XFEM。
英文摘要：
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.
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