Multi-fidelity methods for fluid-structure interaction and uncertainty quantification

Abstract

The cost and turnaround time of the load calculation cycle in the design process of aircraft can be reduced by developing new numerical simulation technologies aimed at efficient prediction of steady and unsteady force coefficients in the flight envelope. In order to capture the most extreme stress levels due to gust and manoeuvres, efficient time-accurate analysis of fluid-structure interaction is desired. In order to incorporate uncertainties in flight conditions, manoeuvres, shape and material properties, efficient uncertainty quantification is desired. This thesis aims at developing efficient multi-fidelity algorithms for fluid-structure interaction and uncertainty quantification. Space-mapping is a multi-fidelity technique that can be applied in order to accelerate strongly coupled partitioned fluid-structure interaction. Gradient-Enhanced Kriging is a response surface technique that can be used for uncertainty quantification. Aggressive Space-Mapping is applied to three academic fluid-structure interaction problems of increasing complexity. For most test cases considered the estimated and observed speedup with respect to the Quasi-Newton algorithm is larger than 1. The influence of the timestep size on the speedup is large compared to other parameters. In case of compressible flows the speedup can rise to 1.5 for large time-steps. In case of incompressible flows higher speedups can be expected due to strong coupling of the fluid-structure interaction. Gradient-Enhanced Kriging (GEK) is applied to two academic uncertainty quantification problems of increasing complexity. The observed speedup of GEK with respect to Kriging increases with the number of dimensions of the design-space. When the gradients are computed with the adjoint method the theoretical speedup is S = (1+d)/2, where d is the number of dimensions. The observed speedup and theoretical speedup are only close if the derivative noise, variation of the sampling plan and the variation of the target accuracies are taken into account.