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Volume 12, Issue 2
Viscoelastic Immersed Boundary Methods for Zero Reynolds Number Flow

Wanda Strychalski & Robert D. Guy

Commun. Comput. Phys., 12 (2012), pp. 462-478.

Published online: 2012-12

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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.

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@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} }
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 -

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.

Wanda Strychalski & Robert D. Guy. (2020). Viscoelastic Immersed Boundary Methods for Zero Reynolds Number Flow. Communications in Computational Physics. 12 (2). 462-478. doi:10.4208/cicp.050211.090811s
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