Adaptive time integration based on an estimated local truncation error in a mid-fidelity aeroelastic simulation framework

Accurately simulating aeroelastic systems while maintaining low computational costs poses a significant challenge, especially when analyzing modern slender structures which exhibit nonlinear behavior. Coupling geometrically exact beams with the unsteady vortex lattice method through a strong fluid-structure interaction provides an attractive trade-off between accuracy and computational effort. However, the robustness of this approach can be limited due to large displacements, rotations, or rapidly changing fluid velocities. In some cases, the convergence of the simulation can be maintained by employing very small time steps, which, however, increase computational costs. Especially when numerous computations need to be performed in a design process, this can hinder the economic viability of this mid-fidelity framework. A method for estimating the local error is introduced, upon which an adaptive time step size control is applied. Our approach combines Richardson's extrapolation with a more accurate approximation of aerodynamic forces. This allows us to determine a reference solution with higher order accuracy and thereby estimate the local error. The adaptive time step size has the key aim of enhancing the framework's robustness. Additionally, this approach can effectively minimize computational costs by reducing the number of required time steps. This is also supported by the fact that no convergence study needs to be carried out in order to find a suitable constant time step. We show these properties in relevant nonlinear examples. The application is user friendly, as only a few parameters need to be set. The local error estimation approach can easily be transferred to other implementations and different time step adaptation algorithms.