Passive concentration dynamics incorporated into the library IB2d, a two-dimensional implementation of the immersed...

Area of Science:

• Fluid dynamics
• Computational science
• Biophysics

Background:

• Simulating fluid-structure interaction with moving boundaries is complex.
• Modeling advection-diffusion of chemical or heat density is crucial in many scientific fields.
• Existing methods may lack flexibility for coupled fluid-structure and transport phenomena.

Purpose of the Study:

• To present IB2d, an open-source software library for simulating advection-diffusion in viscous fluids with moving elastic boundaries.
• To provide a robust and user-friendly tool for fluid-structure interaction problems.
• To demonstrate the library's versatility through diverse examples.

Main Methods:

• Utilized Peskin's immersed boundary method for fully-coupled fluid-structure interaction.
• Employed an immersed boundary-like approach for incorporating source/sink terms at the boundary.
• Solved the advection-diffusion equation numerically using a regularized delta function for boundary-fluid coupling.

Main Results:

• Successfully simulated advection-diffusion with moving elastic boundaries.
• Validated the method with convergence results for a benchmark case (stretching rubber band).
• Demonstrated applicability to biological systems: filter-feeding appendages, heat dissipation in leaves, and gas exchange in soft corals.

Conclusions:

• IB2d offers a powerful and accessible tool for simulating complex fluid dynamics and transport phenomena.
• The immersed boundary method effectively couples fluid motion with chemical/heat transport at elastic boundaries.
• The library has broad applications in life sciences, including biomechanics, environmental science, and developmental biology.