Viscoelastic Immersed Boundary Methods for Zero Reynolds Number Flow

The immersed boundary method has been extensively used to simulate the motion of elastic structures immersed in a viscous fluid.For some applications,such as modeling biological materials,capturing internal boundary viscosity is important.We present numerical methods for simulating Kelvin-Voigt and standard linear viscoelastic structures immersed in zero Reynolds number flow.We find that the explicit time immersed boundary update is unconditionally unstable above a critical boundary to fluid viscosity ratio for a Kelvin-Voigt material.We also show there is a severe time step restriction when simulating a standard linear boundary with a small relaxation time scale using the same explicit update.A stable implicit method is presented to overcome these computation challenges.