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

Viscoelastic Immersed Boundary Methods for Zero Reynolds Number Flow

Wanda Strychalski 1*, Robert D. Guy 1

1 Department of Mathematics, University of California, Davis CA 95616, USA.

Received 5 February 2011; Accepted (in revised version) 9 August 2011
Available online 20 February 2012


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.

AMS subject classifications: 65M06, 65M12, 74F10, 76D07, 76M20

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Key words: Stokes flow, viscoelastic structures, fluid-structure interaction, numerical instability.

*Corresponding author.
Email: (W. Strychalski), (R. D. Guy)

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