The Finite Element Immersed Boundary Method for the Numerical Simulation of the Motion of Red Blood Cells in Microfluidic Flows Numerical Methods for Differential Equations, Optimization, and Technological Problems

We study the mathematical modeling and numerical simulation of the motion of red blood cells (RBCs) subject to an external incompressible flow in a microchannel. RBCs are viscoelastic bodies consisting of a deformable elastic membrane enclosing an incompressible fluid. We study two versions of the Finite Element Immersed Boundary Method (FE-IB), a semi-explicit scheme that requires a CFL-type stability condition and a fully implicit scheme that is unconditionally stable and numerically realized by a predictor-corrector continuation strategy featuring an adaptive choice of the time step sizes. The performance of the two schemes is illustrated by numerical simulations for various scenarios including the tank treading motion in microchannels and the motion through thin capillaries.