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A comprehensive assessment of accuracy of adaptive integration of cut cells for laminar fluid-structure interaction problems

Kadapa, Chennakesava; Wang, Xinyu; Mei, Yue


Xinyu Wang

Yue Mei


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.


Kadapa, C., Wang, X., & Mei, Y. (2022). A comprehensive assessment of accuracy of adaptive integration of cut cells for laminar fluid-structure interaction problems. Computers and Mathematics with Applications, 122, 1-18.

Journal Article Type Article
Acceptance Date Jul 13, 2022
Online Publication Date Aug 1, 2022
Publication Date 2022-09
Deposit Date Aug 29, 2022
Publicly Available Date Aug 30, 2022
Journal Computers & Mathematics with Applications
Print ISSN 0898-1221
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 122
Pages 1-18
Keywords Incompressible Navier-Stokes, Immersed boundary methods, Fluid-structure interaction, CutFEM, Adaptive integration, Flow-induced vibrations
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