TY - GEN
T1 - On the General Analytical Solution of the Kinematic Cosserat Equations
AU - Michels, Dominik L.
AU - Lyakhov, Dmitry
AU - Gerdt, Vladimir P.
AU - Hossain, Zahid
AU - Riedel-Kruse, Ingmar H.
AU - Weber, Andreas G.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work has been partially supported by the Max Planck Society (FKZ-01IMC01/FKZ-01IM10001), the Russian Foundation for Basic Research (16-01-00080), and a BioX Stanford Interdisciplinary Graduate Fellowship. The reviewers’ valuable comments are gratefully acknowledged.
PY - 2016/9/9
Y1 - 2016/9/9
N2 - Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.
AB - Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.
UR - http://hdl.handle.net/10754/621970
UR - http://link.springer.com/chapter/10.1007%2F978-3-319-45641-6_24
UR - http://www.scopus.com/inward/record.url?scp=84988432391&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-45641-6_24
DO - 10.1007/978-3-319-45641-6_24
M3 - Conference contribution
SN - 9783319456409
SP - 367
EP - 380
BT - Computer Algebra in Scientific Computing
PB - Springer Nature
ER -