Complex aeroservoelastic and mechatronic systems imply interaction between multidisciplinary or multifield subcomponents, whose dynamics are characterized by problem- and field-specific time scales and frequency ranges. As opposed to what is usually termed monolithic approach to the simulation of coupled problems, where a single formulation (and software solver) directly models the entire problems, the co-simulation approach allows to exploit state-of-art formulations for specific fields by coupling them as appropriate to establish the required interaction between the subcomponents. The interaction problem between the different and even incompatible interfaces of subcomponent domains can be split in spatial and temporal. This work focuses on the latter aspect. In fact, when subdomains require different time scales to achieve the desired trade-off between accuracy and computational cost, multirate methods can be used to avoid the need of a subdomain solver to comply with excessively stringent requirements resulting from another one. Many multirate methods are designed for monoblock systems and used in single-disciplinary simulations (e.g. electric networks). Their application to co-simulation setups may be not straightforward. A key problem in co-simulation, especially when stability and free response of a system are addressed, as in aeroservoelasticity, is related to the numerical stability of the coupled solution process. This work investigates the linear stability properties of a multirate formulation called ‘Double Extrapolation’ (DE) consisting in integrating each subproblem using second-order accurate, L-stable Backward Difference Formulas (BDF) while each subdomain extrapolates the behavior of the other one. It has been chosen because it allows to eliminate most of the idle time of each subdomain solver. The resulting performance gains are illustrated by applying the proposed method to the simulation of a complex aeroservoelastic system consisting in the aeroelastic model of a Horizontal Axis Wind Turbine (HAWT), developed using the general-purpose multibody formulation implemented in the free solver MBDyn, and a dynamic model of the electric generator, modeled in the free general-purpose block-diagram simulation environment ScicosLab. Both modeling environments are real-time capable; thus the proposed system represents an affordable and versatile solution for the hardware-in-the-loop analysis and design of complex multidisciplinary systems.

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