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Solution techniques for the fully discretized equations in computation of fluid-structure interactions with the space-time formulations. (English) Zbl 1123.76035

Summary: We provide an overview of solution techniques we have developed for fully discretized equations encountered at every time step in computation of fluid-structure interactions with space-time techniques. These coupled nonlinear equations are generated from the finite element discretization of the governing equations for fluid mechanics, structural mechanics and the motion of the fluid mechanics mesh. The fluid mechanics equations are discretized with the deforming-spatial-domain/stabilized space-time formulation. The mesh motion is governed by the equations of elasticity, with smaller elements stiffened in the finite element formulation. The coupled fully discretized equations are solved with the block-iterative, quasi-direct and direct coupling methods. We present numerical examples with incompressible flows and membrane and cable structures.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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