Space-mapping in fluid–structure interaction problems

Abstract

Transient response due to gust loads can lead to structural failure despite the fact that the aero-elastic system is asymptotically stable. Unsteady aeroelastic analysis should therefore be included in the load calculation cycle of the aircraft design process. Especially in the transonic regime, partitioned strong coupling algorithms perform better than loose coupling algorithms and allow larger time-steps in the unsteady simulation. However, the simulation of high fidelity unsteady fluid–structure interaction using strong coupling algorithms is currently too expensive in order to be useful in industry.To accelerate high fidelity partitioned fluid–structure interaction simulations we apply space-mapping, which is a technique that originates from the field of multi-fidelity optimization. Without loss of generality we assume the availability of a cheap low fidelity fluid solver and an expensive high fidelity fluid solver. The space-mapping approach is used to accelerate the high fidelity computation using black-box input/output information of both the high fidelity fluid solver and low fidelity fluid solver. In order to achieve this, a space-mapping function is defined on the fluid–structure interface which keeps track of the differences between the high fidelity model and the low fidelity model during the coupling iterations. Reformulating the root-finding problem on the fluid–structure interaction interface using the space-mapping function results in the Aggressive Space-Mapping algorithm.The Aggressive Space-Mapping algorithm is applied to 1-D and 2-D test cases in order to assess the speedup with respect to the Quasi-Newton Inverse Least Squares algorithm. The latter is considered to be the current state of the art in partitioned strong coupling algorithms. The observed speedup depends mainly on the type of FSI problem and the time step size. The maximum observed speedup is about 1.5.The application of the space-mapping technique to partitioned fluid–structure interaction problems is found to be a promising approach. The framework is non-intrusive and allows the reuse of existing solvers which is especially useful in an industrial environment. It is expected that the space-mapping technique can be combined with higher order time integration schemes that maintain accuracy over a large range of time step sizes.