@Article{CiCP-12-462, author = {}, title = {Viscoelastic Immersed Boundary Methods for Zero Reynolds Number Flow}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {2}, pages = {462--478}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.050211.090811s}, url = {http://global-sci.org/intro/article_detail/cicp/7299.html} }