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On the Lagrangian-Eulerian Coupling in the Immersed Finite Element/Difference Method.

Jae H Lee1,2,3, Boyce E Griffith4,5,6,7

  • 1Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA.

Journal of Computational Physics
|March 18, 2022
PubMed
Summary
This summary is machine-generated.

The choice of kernel function in the immersed boundary (IB) method significantly impacts fluid-structure interaction (FSI) accuracy. Narrower kernels offer greater robustness and accuracy, especially in shear-dominated FSI simulations.

Keywords:
fluid-structure interactionimmersed boundary methodimmersed finite element/difference methodregularized delta functions

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Area of Science:

  • Computational fluid dynamics
  • Fluid-structure interaction (FSI)
  • Numerical methods

Background:

  • The immersed boundary (IB) method is a powerful tool for simulating fluid-structure interaction (FSI).
  • Accurate coupling between fluid and structure relies on discrete approximations of integral transforms using regularized delta function kernels.
  • Previous studies on kernel function impact were limited to simplified scenarios, potentially not reflecting real-world FSI applications at higher Reynolds numbers or varied loading conditions.

Purpose of the Study:

  • To systematically investigate the influence of different regularized delta function kernels on the accuracy of the immersed finite element/difference (IFED) method for FSI.
  • To evaluate the impact of varying relative mesh spacings between the Lagrangian structure and Eulerian fluid grids.
  • To assess kernel performance across a range of benchmark FSI tests, including those with significant pressure loading.

Main Methods:

  • Utilized the immersed finite element/difference (IFED) method, an extension of the IB approach combining finite element for structures and finite difference for fluids.
  • Employed a collection of interaction points for evaluating the regularized delta function, allowing for denser sampling than the structural mesh nodes.
  • Conducted systematic studies across several FSI benchmark tests and a large-scale model of a bioprosthetic heart valve.

Main Results:

  • Kernels satisfying the even-odd condition require higher resolution for comparable accuracy to those that do not.
  • Narrower kernels demonstrate greater robustness, showing less sensitivity to relative mesh spacing variations.
  • Coarser structural meshes achieve high accuracy in shear-dominated flows but not in cases with substantial normal forces.

Conclusions:

  • The selection of regularized delta function kernels and the relative mesh resolutions are critical for achieving accurate FSI simulations with the IFED method.
  • Narrower kernels and careful consideration of mesh ratios are recommended for robust and accurate FSI predictions, particularly in complex flow regimes.
  • Findings were validated using a realistic FSI model of a heart valve, confirming the practical implications of kernel choice and mesh resolution.