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An Immersed Interface Method for Discrete Surfaces.

Ebrahim M Kolahdouz1,2, Amneet Pal Singh Bhalla3, Brent A Craven2

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

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Summary
This summary is machine-generated.

This study introduces a new immersed interface method (IIM) for fluid-structure interaction (FSI) that achieves higher accuracy with simpler geometry representations. The method effectively handles stress discontinuities at fluid-solid interfaces, demonstrated in simulations including blood flow in the inferior vena cava.

Keywords:
complex geometriesfinite elementfluid-structure interactionimmersed boundary methodimmersed interface methodjump conditions

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Area of Science:

  • Computational Fluid Dynamics
  • Biomedical Engineering
  • Numerical Analysis

Background:

  • Fluid-structure interaction (FSI) is crucial in many scientific and engineering fields.
  • Traditional immersed boundary (IB) methods struggle with accuracy at fluid-solid interfaces due to stress discontinuities.
  • Existing immersed interface methods (IIM) often require smooth interface geometry, limiting their application.

Purpose of the Study:

  • To develop an IIM formulation capable of handling complex geometries using only C0 representations.
  • To achieve higher-order accuracy in FSI simulations by sharply imposing stress jump conditions.
  • To demonstrate the method's efficacy in simulating realistic physiological flows.

Main Methods:

  • Introduced a novel immersed interface formulation utilizing C0 representations of the immersed interface.
  • Employed finite element methods for simulating fluid-structure interaction.
  • Verified the method through prescribed interface motion models and simulation of blood flow in an inferior vena cava model.

Main Results:

  • The method sharply resolves stress discontinuities at immersed boundaries without needing analytic geometry information.
  • Achieved global second-order accuracy for pressure and velocity gradient jump conditions.
  • Demonstrated second-order global convergence rates for Eulerian velocity and good agreement with body-fitted methods in inferior vena cava flow simulation.

Conclusions:

  • The developed IIM formulation overcomes limitations of conventional IB methods, offering higher accuracy with simpler geometric requirements.
  • The approach is suitable for complex geometries and realistic physiological simulations, such as blood flow.
  • This method provides a robust and accurate tool for FSI problems in various scientific and engineering domains.