@Article{CiCP-12-2,
author = {},
title = {Simulating an Elastic Ring with Bend and Twist by an Adaptive Generalized Immersed Boundary Method},
journal = {Communications in Computational Physics},
year = {2012},
volume = {12},
number = {2},
pages = {433--461},
abstract = {<p style="text-align: justify;">Many problems involving the interaction of an elastic structure and a viscous fluid can be solved by the immersed boundary (IB) method. In the IB approach
to such problems, the elastic forces generated by the immersed structure are applied to
the surrounding fluid, and the motion of the immersed structure is determined by the
local motion of the fluid. Recently, the IB method has been extended to treat more general elasticity models that include both positional and rotational degrees of freedom.
For such models, force and torque must both be applied to the fluid. The positional
degrees of freedom of the immersed structure move according to the local linear velocity of the fluid, whereas the rotational degrees of freedom move according to the local
angular velocity. This paper introduces a spatially adaptive, formally second-order accurate version of this generalized immersed boundary method. We use this adaptive
scheme to simulate the dynamics of an elastic ring immersed in fluid. To describe the
elasticity of the ring, we use an unconstrained version of Kirchhoff rod theory. We
demonstrate empirically that our numerical scheme yields essentially second-order
convergence rates when applied to such problems. We also study dynamical instabilities of such fluid-structure systems, and we compare numerical results produced by
our method to classical analytic results from elastic rod theory.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.190211.060811s},
url = {https://global-sci.com/article/80781/simulating-an-elastic-ring-with-bend-and-twist-by-an-adaptive-generalized-immersed-boundary-method}
}