Energy-based monitoring and correction to enhance the accuracy and stability of explicit co-simulation

The simulation of complex engineering applications often requires the consideration of component-level dynamics whose nature and time-scale differ across the elements of which the system is composed. Co-simulation offers an effective approach to deal with the modelling and numerical integration of such assemblies by assigning adequate description and solution methods to each component. Explicit co-simulation, in particular, is frequently used when efficient code execution is a requirement, for instance in real-time setups. Using explicit schemes, however, can lead to the introduction of energy artifacts at the discrete-time interface between subsystems. The resulting energy errors deteriorate the accuracy of the co-simulation results and may in some cases develop into the instability of the numerical integration process. This paper discusses the factors that influence the severity of the energy errors generated at the interface in explicit co-simulation applications, and presents a monitoring and correction methodology to detect and remove them. The method uses only the information carried by the variables exchanged between the subsystems and the co-simulation manager. The performance of this energy-correction technique was evaluated in multi-rate co-simulation of mechanical and multiphysics benchmark examples.