A fixed-grid b-spline finite element technique for fluid-structure interaction - Rüberg, T.; Cirak, F. (International journal for numerical methods in fluids, 2014)
SUMMARYWe 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. 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 using isoparametric b‐spline basis functions defined on a logically Cartesian grid. The beam equations are discretised with b‐splines, and the shell equations with subdivision basis functions, both leading to a rotation‐free formulation.