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

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.