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In this thesis, a coupled multiphysical system is considered, whereas the focus is upon aeroelastic problems. For a consistent formulation of such coupled systems, an energy based variational formulation is chosen to describe initially the structural and fluid subsystem by Hamilton's principle. Both basic fluid model equations - inviscid and viscous fluid models - are employed by this weak variational energy principle. This procedure allows to describe the coupled problem by the classical direct two-field approach as well as by a novel indirect three-field approach. To discretize the entire system consistently with finite elements, the CBS scheme is employed for the fluid domain described by the Navier-Stokes equation in ALE frame of reference. This allows the fluid domain to be temporally deformable, which is essential for aeroelastic computations. The CBS scheme is verified for a wide range of typical fluid problems ranging from inviscid, viscous, incompressible and turbulent flows. A good agreement with data published in literature and with the further solver TAU are found, which underlines the applicability of the CBS scheme for different fluid flow models. The DG-CBS scheme as a novel and attractive approach has been derived from the continuous version. One important advantage of the DG version is the design of the element edge flux to be locally conservative. For the example of the laminar flow over the NACA0012 airfoil as well as for the panel flutter problem, a comparison of the CBS and DG-CBS scheme is made on structured fluid grids including grid convergence studies. With biquadratic, more accurate results in terms of the flutter frequency are obtained with DG-CBS scheme. Moreover, no global system of linear equations needs to be solved at the computational expense of addidtional element edge flux calculations with the DG version. This might be attractive for fluid grids with a high number of degrees of freedom. Consequently, the whole coupled system is further discretized with finite elements including the structural subdomain, the deformation of the fluid grid and the transfer scheme. For the fluid grid deformation, it is found, that all of the presented stiffness evaluation methods perform similarly. The stiffness strategy based on the wall distance and the characteristic length is recommended to be used for the simple testcases with the unstructured grid. For a structured grid around an airfoil, the best grids are obtained with the stiffness methods based on the wall distance. Thus, for general fluid grid deformations, the method, which use a combination of the wall distance and the characteristic length, can be recommended and is hence applied for the panel flutter problem. Based on the unified weak variational coupling schemes, several data transfer schemes are introduced, which share the property of load and energy conservation. With a h-refinement of the integration grid, a significant reduction of the transfer error is observed for low-curved interface meshes. The decrease of the transfer error is limited by the facetting error, which is identified for highly curved interface meshes and for a realistic wing configuration. For the panel flutter problem at Ma∞ = 1.0 and rp = 170, the Galerkin and the dual-Lagrange based transfer as well as the conservative interpolation gives similar results in terms of the frequency and amplitude of the LCO. With its local accuracy together with a global load conservation property and due to the efficiency of a matrix-free transfer scheme, the dual-Lagrange based transfer is an attractive approach for the data transmission of the coupled system. A smooth transfer scheme is proposed, which uses the novel three-field coupling approach with a higher spatial order discretization of the connectivity frame. Regarding the time integration and equilibrium iteration, the three-field approach is assessed for a strongly coupled problem. With the use of the Newton-GMRES iteration scheme, the number of DN cycles is reduced for |
