Finite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are cut by the interface between two different domains need to be integrated using special techniques in order to obtain optimal convergence rates and accurate fluxes across the interface. The adaptive integration technique in which the cells are recursively subdivided is one of the popular techniques for the numerical integration of cut-cells due to its advantages over tessellation, particularly for problems involving complex geometries in three dimensions. Although adaptive integration does not impose any limitations on the representation of the geometry of immersed solids as it requires only point location algorithms, it becomes computationally expensive for recovering optimal convergence rates. This paper presents a comprehensive assessment of the adaptive integration of cut-cells for applications in computational fluid dynamics and fluid-structure interaction. We assess the effect of the accuracy of integration of cut cells on convergence rates in velocity and pressure fields, and then on forces and displacements for fluid-structure interaction problems by studying several examples in two and three dimensions. By taking the computational cost and the accuracy of forces and displacements into account, we demonstrate that numerical results of acceptable accuracy for FSI problems involving laminar flows can be obtained with only fewer levels of refinement. In particular, we show that three levels of adaptive refinement are sufficient for obtaining force and displacement values of acceptable accuracy for laminar fluid-structure interaction problems.

翻译：以切割细胞为基础的精密元素方法越来越受欢迎,因为其优于基于体装模具的配方,其优点在于用于处理移动界面的问题。在这种方法中,由于两个不同领域之间的接口而剪切的细胞(或元素)需要使用特殊技术加以整合,以便获得最佳汇合率和整个接口的准确通量。细胞循环分解的适应性集成技术,是切割细胞因优于熔融而进行数字集成的流行技术之一,特别是对于涉及三个方面复杂地貌的问题而言。虽然适应性整合并不限制浸透固体的几何精确度,因为它只要求点位置算法,但对于恢复最佳汇合率而言,计算成本成本成本成本成本成本成本成本成本和流动性的偏移率,然后通过研究精度的两个和三个层次的精确度来评估流结构互动问题。我们通过计算精确度的精确度,只能用精确度来显示可接受的流流流的精确度,我们只能通过精确度的精确度来评估流流的精确度。