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Hybrid finite difference/finite element immersed boundary method.

Boyce E Griffith1, Xiaoyu Luo2

  • 1Departments of Mathematics and Biomedical Engineering, Carolina Center for Interdisciplinary Applied Mathematics, and McAllister Heart Institute, University of North Carolina, Chapel Hill, NC, USA.

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|April 21, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces a new coupling scheme for the immersed boundary method (IBM) that allows for independent spatial discretizations of structures and fluid grids. This approach enables the use of coarser structural meshes, significantly reducing discretization errors in fluid-structure interaction simulations.

Keywords:
finite difference methodfinite element methodfluid-structure interactionimmersed boundary methodincompressible elasticityincompressible flow

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Area of Science:

  • Computational fluid dynamics
  • Multiphysics simulation
  • Biomedical engineering

Background:

  • The immersed boundary method (IBM) couples fluid and structure dynamics using Lagrangian and Eulerian descriptions.
  • Traditional IBM requires fine Lagrangian meshes, often finer than the Eulerian grid, increasing computational cost.
  • Existing methods face challenges in efficiently handling complex structural deformations and discretizations.

Purpose of the Study:

  • To develop a novel coupling scheme for the immersed boundary method that decouples structural and fluid grid discretizations.
  • To enable the use of coarser Lagrangian structural meshes without compromising accuracy in fluid-structure interaction (FSI) simulations.
  • To improve the efficiency and applicability of the immersed boundary method for complex FSI problems.

Main Methods:

  • Introduced a finite element discretization for the structure coupled with a finite difference scheme for the fluid.
  • Developed a Lagrangian-Eulerian coupling scheme facilitating independent spatial discretizations.
  • Applied the method to benchmark problems including elastic, rigid, and actively contracting structures, and an idealized left ventricle model.
  • Contrasted two weak forms of the governing equations to identify the most effective for coarse structural discretizations.

Main Results:

  • Demonstrated that coarser Lagrangian structural meshes can yield significantly smaller discretization errors compared to finer meshes.
  • Achieved discretization errors several orders of magnitude smaller with coarser meshes in specific test cases.
  • Validated the effectiveness of the new coupling approach for fluid-structure interaction simulations.
  • Identified a superior weak form for coarse structural discretizations within the developed coupling scheme.

Conclusions:

  • The developed Lagrangian-Eulerian coupling approach effectively integrates independent spatial discretizations for fluid-structure interaction using the immersed boundary method.
  • This method allows for the successful use of coarser structural meshes, leading to substantial reductions in discretization errors and computational cost.
  • The findings pave the way for more efficient and accurate simulations of complex fluid-structure interaction phenomena, particularly in biomedical applications.