An Immersed Interface Method for Discrete Surfaces.

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.