Performance Improvement of Explicit Co-simulation Methods Through Continuous Extrapolation

In order to couple several simulation models, the corresponding software tools can be interconnected by means of a co-simulation. The inputs and outputs of the models depend on each other and have to be updated during the time integration process of the numerical solvers. Since the tools can only communicate at discrete macro-time points, the model inputs are mostly approximated, e.g., by using polynomial interpolation and extrapolation techniques. As a drawback of classical extrapolation methods, discontinuities occur at the macro-time points. This can slow down the solvers and reduces the efficiency of the co-simulation. The current paper considers continuous approximation techniques of C-0, C-1 and C-2 type which are capable to overcome the discontinuity issues. The approaches are analyzed regarding numerical stability, global error and performance. To show the benefit of the continuity, the methods are implemented in a master-slave co-simulation and a comparison with the classical discontinuous approach is done. The C-2-continuous approach mostly outperforms the methods of lower continuity. The C-0-continuous method fails due to a limitation of the error order. With a here-presented enhancement the order drop of the C-0-continuous method can be avoided.