  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.
