Adaptive time-step control for nonlinear fluid-structure interaction

In this work, we consider time step control for variational-monolithic fluid-structure interaction. The fluid-structure interaction (FSI) system is based on the arbitrary Lagrangian-Eulerian approach and couples the incompressible Navier-Stokes equations with geometrically nonlinear elasticity resulting in a nonlinear PDE system. Based on the monolithic setting, we develop algorithms for temporal adaptivity that are based on a rigorous derivation of dual-weighted sensitivity measures and heuristic truncation-based time step control. The Fractional-Step-theta scheme is the underlying time-stepping method. In order to apply the dual-weighted residual method to our setting, a Galerkin interpretation of the Fractional-Step-theta scheme must be employed. All developments are substantiated with several numerical tests, namely FSI-benchmarks, including appropriate extensions, and a flapping membrane example.