# Lubricated Immersed Boundary Method in Two Dimensions

## TL;DR

This paper introduces a lubricated immersed boundary method for 2D fluid-structure interaction problems involving thin fluid layers, achieving higher accuracy and better capturing vesicle dynamics near walls.

## Contribution

The paper develops a novel immersed boundary method incorporating lubrication theory, improving accuracy in simulating near-contact elastic structures in fluid flows.

## Key findings

- Achieves 2nd-order convergence in simple flows.
- Effectively simulates vesicle near walls in shear flow.
- Captures vesicle motion through narrow channels on coarse grids.

## Abstract

Many biological examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen and the intracellular trafficking of vesicles into dendritic spines, involve the near-contact of elastic structures separated by thin layers of fluid. Motivated by such problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We demonstrate 2nd-order accurate convergence for simple two-dimensional flows with known exact solutions to showcase the increased accuracy of this method compared to the standard immersed boundary method. Motivated by the phenomenon of wall-induced migration, we apply the lubricated immersed boundary method to simulate an elastic vesicle near a wall in shear flow. We also simulate the dynamics of a vesicle traveling through a narrow channel and observe the ability of the lubricated method to capture the vesicle motion on relatively coarse fluid grids.