Space-time discretization for Fluid-Structure Interaction

Accurate numerical prediction of aeroelastic instabilities requires correct representation of the transfer of energy between the fluid and the structure, particularly when determining the neutral-stability point. In the numerical model, energy transfer depends on the discretization methods used for the fluid and the structure as well as on their coupling. In this paper we consider a space-time Galerkin least-squares formulation of the fluid equations and use shape functions which are discontinuous in time. For the time integration of the structure we investigate two essentially different methods, namely the trapezoidal method and a time-discontinuous Galerkin method. In particular, we assess their ability to conserve energy in the presence of a forcing term. Further, we show that these methods are different in their ability to conserve momentum and energy at the interface when coupled to the fluid discretization, We compare monolithic and partitioned fluid-structure coupling. Partitioned schemes are typically unstable. Structural prediction can improve their accuracy and stability, but the admissible time step still remains restricted. Although monolithic schemes do not necessarily imply energy conservation at the interface, they appear to have better stability properties than partitioned schemes allowing for larger time steps. Moreover, we show that the efficiency of the iterative solver employed in a monolithic scheme can be improved by prediction techniques. We illustrate our results by numerical experiments for a one-dimensional model problem of a piston interacting with a fluid.