Nonlinear Aeroelasticity Computations in Transonic Flows Using Tightly Coupling Algorithms

A nonlinear computational aeroelasticity model based on the Euler equations of compressible flows and the linear elastodynamic equations for structures is developed. The Euler equations are solved on dynamic meshes using the ALE kinematic description. Thus, the mesh constitutes another field governed by pseudo-elatodynamic equations. The three fields are discretized using proper finite element formulations which satisfy the geometric conservation law. A matcher module is incorporated for the purpose of pairing the grids on the fluid-structure interface and for transferring the loads and displacements between the fluid and structure solvers. Two solutions strategies (Gauss Seidel and Schur-Complement) for solving the nonlinear aeroelastic system are discussed. Using second order time discretization schemes allows us to use large time steps in the computations. The numerical results on the AGARD 445.6 aeroelastic wing compare well with the experimental ones and show that the Schur-complement coupling algorithm is more robust than the Gauss-Seidel algorithm for relatively large oscillation amplitudes.