Co-Simulation: Error Estimation and Macro-Step Size Control

T. Meyer, J. Kraft,  and B. Schweizer (February 24, 2021). "Co-Simulation: Error Estimation and Macro-Step Size Control." ASME. J. Comput. Nonlinear Dynam. April 2021; 16(4): 041002. https://doi.org/10.1115/1.4048944

Co-simulation techniques are commonly used to analyze multidisciplinary and multiphysical systems as well as to parallelize dynamical simulation models. Therefore, the overall system is decomposed into a certain number of subsystems. To define the coupling between the subsystems, coupling equations and appropriate coupling variables have to be specified. Moreover, a communication-time grid has to be introduced by defining macro-time points . The subsystems are integrated independently between the communication-time points; coupling variables are only exchanged at the macro-time points. The crucial point in connection with equidistant communication-time grids, which are frequently used in practical applications, is the appropriate choice of the macro-step size. Efficiency and accuracy of a co-simulation may, however, considerably be increased by using a variable communication-time grid. Therefore, an error estimator for controlling the macro-step size is required. Here, different error estimators for explicit and implicit co-simulation schemes are derived and incorporated into the macro-step size control algorithm. Numerical studies clearly demonstrate that the main problems associated with equidistant macro-grids – namely a trade-off between stability/accuracy and efficiency – disappear, if variable communication-time grids are used. The manuscript focuses on mechanical co-simulation models. The basic results may, however, also be applied to arbitrary, non-mechanical co-simulation models.