A fixed-grid b-spline finite element technique for fluid–structure interaction
Article first published online: 13 DEC 2013
Copyright © 2013 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids
Volume 74, Issue 9, pages 623–660, 30 March 2014
How to Cite
Rüberg, T. and Cirak, F. (2014), A fixed-grid b-spline finite element technique for fluid–structure interaction. Int. J. Numer. Meth. Fluids, 74: 623–660. doi: 10.1002/fld.3864
- Issue published online: 9 FEB 2014
- Article first published online: 13 DEC 2013
- Manuscript Accepted: 2 OCT 2013
- Manuscript Received: 4 AUG 2013
- finite elements;
- fluid–structure interaction;
- pressure–correction method;
- isogeometric analysis
We present a fixed-grid finite element technique for fluid–structure interaction problems involving incompressible viscous flows and thin structures. The flow equations are discretised with isoparametric b-spline basis functions defined on a logically Cartesian grid. In addition, the previously proposed subdivision-stabilisation technique is used to ensure inf–sup stability. The beam equations are discretised with b-splines and the shell equations with subdivision basis functions, both leading to a rotation-free formulation. The interface conditions between the fluid and the structure are enforced with the Nitsche technique. The resulting coupled system of equations is solved with a Dirichlet–Robin partitioning scheme, and the fluid equations are solved with a pressure–correction method. Auxiliary techniques employed for improving numerical robustness include the level-set based implicit representation of the structure interface on the fluid grid, a cut-cell integration algorithm based on marching tetrahedra and the conservative data transfer between the fluid and structure discretisations. A number of verification and validation examples, primarily motivated by animal locomotion in air or water, demonstrate the robustness and efficiency of our approach. Copyright © 2013 John Wiley & Sons, Ltd.