Lubricated Immersed Boundary Method in Two Dimensions
This method addresses the challenge of simulating fluid-structure interactions with near-contact elastic structures, which is relevant for biological problems like red blood cell transit and intracellular trafficking.
The authors introduce a lubricated immersed boundary method that uses lubrication theory to resolve thin fluid layers between elastic structures, demonstrating 2nd-order accurate convergence and improved accuracy over the standard method in 2D flows. The method captures vesicle motion near walls and through narrow channels on coarse grids.
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.