Expectations about the efficiency and the level of detail delivered by the simulation of engineering applications continue to grow steadily, in parallel with the increase in computational power and resources that are available to researchers. Moreover, complex engineering projects often require the consideration of multiphysics phenomena. Co-simulation, or solver coupling, enables the efficient numerical integration of complex engineering applications composed of subsystems with different physical properties and behaviour. In co-simulation setups, the dynamics of each subsystem is integrated by its own dedicated solver. Communication between solvers takes place at discrete-time intervals, through the exchange of a limited set of coupling variables. The internals of each subsystem remain thus undisclosed to the rest of the co-simulation environment. Co-simulation is modular and enables the distribution of computational workload between several processing units.  Besides, it is convenient to protect intellectual property, as the implementation details of the solvers and models used inside the coupled subsystems do not need to be disclosed to other simulators in the environment nor to the co-simulation manager. However, the discrete-time nature of the coupling interface inherently leads to the introduction of delays and discontinuities in the coupling variables, which affect negatively the accuracy of the numerical integration and may eventually cause it to become unstable, particularly in the case of explicit, non-iterative co-simulation schemes.

Several methods have been proposed in the literature to detect and prevent instability in explicit co-simulation setups. Non-iterative co-simulation is particularly prone to introducing energy errors at the coupling interface. Integration steps in the subsystems cannot be repeated or corrected, and so discontinuities are introduced in the coupling variables at each communication point. Monitoring energy exchanges at the interface is a way to detect the accumulation of errors and to define methods to keep the numerical integration stable, e.g., adjusting the size of the communication step, or modifying the subsystem inputs to remove the surplus energy introduced by the co-simulation scheme.

In this research, we use energy indicators to monitor the effect of co-simulation schemes and coupling options, such as the input extrapolation order, on the overall simulation stability. Energy correction approaches can be developed based on the information provided by these indicators. Special adjustments are required when subsystems extrapolate their inputs or multirate co-simulation schemes are used. A set of benchmark problems was defined and used to assess the ability of the selected methods to detect stability issues in explicit co-simulation setups and to address them without compromising the accuracy of the simulation.


Use of Energy Indicators in the Explicit Co-Simulation of Multibody Systems

Division / Sponsors: 
Design Engineering Division and Computers & Information In Engineering Division


Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2020/volume/83907

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