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A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction.

Ebrahim M Kolahdouz1, David R Wells2, Simone Rossi2

  • 1Center for Computational Biology, Flatiron Institute, Simons Foundation, New York, NY, USA.

Journal of Computational Physics
|May 22, 2023
PubMed
Summary
This summary is machine-generated.

This study presents a new immersed Lagrangian-Eulerian (ILE) method for simulating fluid-structure interaction (FSI) with flexible bodies. The flexible-body immersed Lagrangian-Eulerian (ILE) approach accurately models complex FSI phenomena, including blood clot transport.

Keywords:
Fluid-structure interactionimmersed Lagrangian-Eulerian methodimmersed interface methodinferior vena cava filternonlinear continuum mechanics

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Area of Science:

  • Computational fluid dynamics
  • Solid mechanics
  • Fluid-structure interaction (FSI)

Background:

  • Simulating fluid-structure interaction (FSI) with flexible bodies presents challenges, especially with nonlinear material models and varying mass density ratios.
  • Existing immersed boundary (IB) methods often lack the accuracy of body-fitted approaches in resolving stresses at the fluid-structure interface.

Purpose of the Study:

  • To introduce a novel sharp-interface immersed Lagrangian-Eulerian (ILE) scheme for simulating FSI with flexible bodies.
  • To extend previous work on rigid-body FSI to accommodate general nonlinear material models and a wide range of mass density ratios.

Main Methods:

  • The flexible-body ILE scheme combines the geometric flexibility of IB methods with accurate interface stress resolution.
  • Distinct momentum equations for fluid and solid subregions are coupled using a Dirichlet-Neumann strategy.
  • An immersed interface method (IIM) is employed for stress jump conditions, enabling efficient structured-grid solvers for incompressible Navier-Stokes equations.
  • Finite element analysis is used for large-deformation nonlinear elasticity of the solid structures.

Main Results:

  • The ILE formulation achieves accuracy comparable to body-fitted methods while maintaining the flexibility of IB approaches.
  • The penalty approach with distinct interface representations simplifies linear solvers and enables multi-rate time stepping.
  • Grid convergence studies demonstrate second-order accuracy in volume conservation and interface discrepancies, and first/second-order accuracy in structural displacements.
  • Validation against FSI benchmarks and application to blood clot transport in an inferior vena cava filter showcase the method's robustness and accuracy.

Conclusions:

  • The developed flexible-body ILE scheme provides a robust and accurate approach for simulating complex FSI problems.
  • The method's ability to handle nonlinear materials, diverse density ratios, and realistic scenarios like blood clot transport highlights its broad applicability.
  • This sharp-interface approach offers a powerful tool for advancing research in various fields involving fluid-structure interactions.