A radial basis function (RBF)-based ghost cell method is presented to simulate flows around a rigid or flexible moving hydrofoil on a Cartesian grid. A compactly supported radial basis function (CSRBF) is introduced to the ghost cell immersed boundary method to treat the complex flexible boundaries in the fluid. The results indicate that this RBF representation method can accurately track tempo-spatially varied interfaces and avoid the identification failure encountered in original RBF. In addition, an interface cell interpolation method is developed to treat the irregular boundaries such as sharp points and thin boundaries. Solution quality is improved by constructing the interface cells along the local irregular boundaries, instead of the ghost cells. To validate the proposed method, uniform flows around stationary and pitching hydrofoils are simulated. Then, a flexible hydrofoil undulating in the fluid is simulated. Good agreements are obtained by comparing the present results with the reference results. Furthermore, the relationship between the oscillation frequency and the force coefficient is studied. Also, generation mechanism of the thrust force is explained.

中文翻译：

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一种基于径向基函数的复杂刚性或柔性移动边界流的幻像元方法

提出了一种基于径向基函数 (RBF) 的幻像单元方法来模拟笛卡尔网格上刚性或柔性移动水翼周围的流动。将紧支撑径向基函数（CSRBF）引入鬼胞浸没边界法处理流体中复杂的柔性边界。结果表明，该RBF表示方法可以准确地跟踪时空变化的界面，避免了原始RBF中遇到的识别失败。此外，还开发了一种界面单元插值方法来处理不规则边界，如尖点和细边界。通过沿局部不规则边界构建界面单元而不是重影单元来提高解决方案质量。为了验证所提出的方法，模拟围绕静止和俯仰水翼的均匀流动。然后，模拟在流体中起伏的柔性水翼。通过将当前结果与参考结果进行比较，获得了良好的一致性。此外，研究了振荡频率与力系数之间的关系。另外，对推力的产生机理进行了说明。