The numerical simulation of coupled multi-field problems is increasingly gaining interest. In aeroelasticity, the interaction of an elastic structure with its surrounding air flow is investigated. Whereas much previous research has focused on staggered solution procedures, in the present work a coupled space-time finite element method for transonic aeroelasticity is developed in order to eliminate limitations for highly unsteady, strongly coupled and nonlinear problems. An efficient, block-iterative solver based on the nonlinear iterations of the subdomains is used. The employed time-discontinuous GALERKIN discretization enforces the initial conditions of each time slab in weak sense and is implicit, unconditionally stable and higher order accurate in time. Furthermore, dynamic meshes for the deforming fluid domain are easily implemented and geometric conservation is automatically satisfied.
GALERKlN/least-squares stabilization is applied to obtain accurate solutions for both elliptic and hyperbolic partial differential equations. Thereby, appropriate up-winding of the convective terms of the flow equations is attained. Nonlinear and consistent higher order discontinuity capturing operators are applied to guarantee mono-tonic solutions at shocks in transonic flow. The variationally consistent formulation of inviscid flow boundary conditions at curved boundary contours and sharp corners is investigated for improved accuracy. In elastodynamics, GALERKlN/generalized least-squares stabilization is designed to enhance the resolution of elastic wave propagation.