Solution techniques for the fully discretized equations in computation of fluid–structure interactions with the space–time formulations

We provide an overview of the solution techniques we have developed for the fully discretized equations encountered at every time step in computation of fluid–structure interactions with the space–time techniques. These coupled, nonlinear equations are generated from the finite element discretization of the governing equations for the 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 the 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.