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Viscoelastic Immersed Boundary Methods for Zero Reynolds Number Flow

Published online by Cambridge University Press:  20 August 2015

Wanda Strychalski  and
Robert D. Guy
Wanda Strychalski*
Affiliation:
Department of Mathematics, University of California, Davis CA 95616, USA
Robert D. Guy*
Affiliation:
Department of Mathematics, University of California, Davis CA 95616, USA
*
Corresponding author.Email:wanda@math.ucdavis.edu
Email:guy@math.ucdavis.edu
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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.

Keywords

65M0665M1274F1076D0776M20Stokes flowviscoelastic structuresfluid-structure interactionnumerical instability

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Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 2 , August 2012 , pp. 462 - 478
Copyright
Copyright © Global Science Press Limited 2012

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