2020/03/18 by Ondrej Maxian, Maxian, Ondrej, Charles S. Peskin +1
Engineering · Materials Science · #65M12 #74F10 #76D07 #FOS: Mathematics #Fluid Dynamics and Vibration Analysis #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA) #Surface Modification and Superhydrophobicity
paper · pdf · doi:10.48550/arxiv.2003.08216
openalex publication_date 2020/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The immersed boundary method is a numerical and mathematical formulation for\nsolving fluid-structure interaction problems. It relies on solving fluid\nequations on an Eulerian fluid grid and interpolating the resulting velocity\nback onto immersed structures. To resolve slender fibers, the grid spacing must\nbe on the order of the fiber radius, and thus the number of required grid\npoints along the filament must be of the same order as the aspect ratio.\nSimulations of slender bodies using the IB method can therefore be intractable.\nA technique is presented to address this problem in the context of Stokes flow.\nThe velocity of the structure is split into a component coming from the\nunderlying fluid grid, which is coarser than normally required, and a component\nproportional to the force (a drag term). The drag coefficient is set so that a\nsingle sphere is represented exactly on a grid of arbitrary meshwidth. Implicit\ntreatment of the drag term removes some of the stability restrictions normally\nassociated with the IB method. This comes at a loss of accuracy, although tests\nare conducted that show 1-2 digits of relative accuracy can be obtained on\ncoarser grids. After its accuracy and stability are tested, the method is\napplied to two real world examples: fibers in shear flow and a suspension of\nfibers. These examples show that the method can reproduce existing results and\nmake reasonable predictions about the viscosity of an aligned fiber suspension.\n