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.

基于切割单元的有限元方法正变得越来越流行，因为它们优于基于贴体网格的公式来解决移动界面的问题。在这种方法中，需要使用特殊技术对被两个不同域之间的界面切割的单元（或元素）进行集成，以获得最佳的收敛速度和跨界面的准确通量。递归细分单元格的自适应积分技术是切割单元格数值积分的流行技术之一，因为它优于曲面细分，特别是对于涉及三维复杂几何形状的问题。尽管自适应积分只需要点定位算法，因此不会对浸入固体的几何表示施加任何限制，但恢复最佳收敛速度的计算成本很高。本文全面评估了切割单元在计算流体动力学和流固耦合中的应用的自适应集成。我们通过研究二维和三维的几个例子来评估切割单元的积分精度对速度和压力场收敛速度的影响，然后对流固耦合问题的力和位移的影响。通过考虑计算成本以及力和位移的准确性，我们证明了对于涉及层流的 FSI 问题的可接受精度的数值结果只需较少的细化级别即可获得。特别是，我们表明三个级别的自适应细化足以获得层流-结构相互作用问题可接受精度的力和位移值。