Viscoelastic Immersed Boundary Methods for Zero Reynolds Number Flow (Communications in Computational Physics, 2020)
The immersed boundary method has been extensively used to simulate themotion of elastic structures immersed in a viscous fluid. For some applications, such asmodeling biological materials, capturing internal boundary viscosity is important. Wepresent numerical methods for simulating Kelvin-Voigt and standard linear viscoelastic structures immersed in zero Reynolds number flow. We find that the explicit timeimmersed boundary update is unconditionally unstable above a critical boundary tofluid viscosity ratio for a Kelvin-Voigt material. We also show there is a severe timestep restriction when simulating a standard linear boundary with a small relaxationtime scale using the same explicit update. A stable implicit method is presented toovercome these computation challenges.