TY - JOUR
T1 - Viscoelastic Immersed Boundary Methods for Zero Reynolds Number Flow
JO - Communications in Computational Physics
VL - 2
SP - 462
EP - 478
PY - 2012
DA - 2012/12
SN - 12
DO - http://doi.org/10.4208/cicp.050211.090811s
UR - https://global-sci.org/intro/article_detail/cicp/7299.html
KW - 
AB - <p style="text-align: justify;">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.</p>