A method for computational aeroelasticity in the time domain has been developed. Time-discontinuous Galerkin space-time finite elements have been employed for both the transonic fluid flow and the elastic aircraft wing structure. The resulting implicit time marching scheme is robust and higher order accurate.
In order to stabilize the convective term of the fluid flow and the elastic wave propagation phenomena in the structure a Galerkin least-squares term is added. For handling discontinuities, a consistent high order nonlinear shock-capturing viscosity is applied. The aerodynamics are modeled using the compressible Euler equations. Nonlinear Timoshenko beam elements are employed for the structure. The time dependent deformation of the fluid domain is modeled using space-time mappings for the FE geometry.
Based on the discretization of equal type for the fluid and the structure, an overall iterative solver strategy for the fully coupled problem is proposed. In each time step, a common loop combines the linearization of the fluid, structure and their coupling conditions. The iterative solution of the resulting linear subproblems is partly done by multigrid methods.