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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  • Abstract

The immersed boundary method has been extensively used to simulate the motion of elasticstructures immersed ina viscous fluid. For some applications, suchas 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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COPYRIGHT: © Global Science Press

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