Viscoelastic Immersed Boundary Methods for Zero Reynolds Number Flow
Wanda Strychalski 1*, Robert D. Guy 11 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
Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164
Key words: Stokes flow, viscoelastic structures, fluid-structure interaction, numerical instability.
Email: email@example.com (W. Strychalski), firstname.lastname@example.org (R. D. Guy)