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Adaptive time-step control for nonlinear fluid-structure interaction. (English) Zbl 1406.76048
Summary: 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.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
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