Abstract A novel iterative direct-forcing immersed boundary (IB) method, which meets the divergence-free and no-slip conditions simultaneously, is proposed in the finite element framework for incompressible flow problems. The coupled velocity and the pressure of the fluid field are solved by the Characteristic-based Split scheme. The formulation for the extra body force is derived according to the no-slip boundary condition. The novelty of the proposed IB method lies in that the calculation of the pressure, the iterations of the velocity, the pressure and the extra body force are accomplished in a loop at the same time. Therefore, the divergence-free and no-slip conditions are ensured fully at the same time. The accuracy of the current IB method is verified by several cases, including static and moving boundaries. Meanwhile, the contributing factors of the spurious force oscillations for moving boundaries are studied. A brand-new viewpoint is proposed, which is different with the common standpoint. The major source of spurious force oscillations pointed out in this paper is that the change of interpolation coefficients when boundaries sweep within an element, instead of the change of interpolation points when boundaries move across adjacent elements, as discussed in existing references. The oscillations which are caused by the inherent properties of the immersed boundary method cannot be avoided, while effective methods can be employed to suppress them, including refining the meshes and applying a proper discrete delta function.

中文翻译：

---

移动体有限元框架下的迭代无散度浸入边界法

摘要 针对不可压缩流动问题，提出了一种同时满足无发散和无滑移条件的迭代直接强迫浸入边界(IB)方法。流体场的耦合速度和压力由基于特征的拆分方案求解。额外体力的公式是根据无滑移边界条件导出的。所提出的IB方法的新颖之处在于压力的计算，速度的迭代，压力的迭代和额外的体力同时在一个循环中完成。因此，同时充分保证了无发散和无滑移条件。当前 IB 方法的准确性通过几种情况进行验证，包括静态和移动边界。同时，研究了移动边界虚假力振荡的影响因素。提出了一种全新的观点，不同于一般的观点。本文指出的虚假力振荡的主要来源是边界在单元内扫掠时插值系数的变化，而不是现有参考文献中讨论的边界跨相邻单元时插值点的变化。浸入边界法固有特性引起的振荡无法避免，但可以采用有效的方法来抑制它们，包括细化网格和应用适当的离散 delta 函数。这与共同的立场不同。本文指出的虚假力振荡的主要来源是边界在单元内扫掠时插值系数的变化，而不是现有参考文献中讨论的边界跨相邻单元时插值点的变化。浸入边界法固有特性引起的振荡无法避免，但可以采用有效的方法来抑制它们，包括细化网格和应用适当的离散 delta 函数。这与共同的立场不同。本文指出的虚假力振荡的主要来源是边界在单元内扫掠时插值系数的变化，而不是现有参考文献中讨论的边界跨相邻单元时插值点的变化。浸入边界法固有特性引起的振荡无法避免，但可以采用有效的方法来抑制它们，包括细化网格和应用适当的离散 delta 函数。如现有参考文献中所述。浸入边界法固有特性引起的振荡无法避免，但可以采用有效的方法来抑制它们，包括细化网格和应用适当的离散 delta 函数。如现有参考文献中所述。浸入边界法固有特性引起的振荡无法避免，但可以采用有效的方法来抑制它们，包括细化网格和应用适当的离散 delta 函数。