F$$_3$$ORNITS : a flexible variable step size non-iterative co-simulation method handling subsystems with hybrid advanced capabilities

This paper introduces the F3ORNITS non-iterative co-simulation algorithm in which F3 stands for the 3 flexible aspects of the method: flexible polynomial order representation of coupling variables, flexible time-stepper applying variable co-simulation step size rules on subsystems allowing it and flexible scheduler orchestrating the meeting times among the subsystems and capable of asynchronousness when subsystems constraints requires it. The motivation of the F3ORNITS method is to accept any kind of co-simulation model, including any kind of subsystem, regardless on their available capabilities. Indeed, one the major problems in industry is that the subsystems usually have constraints or lack of advanced capabilities making it impossible to implement most of the advanced co-simulation algorithms on them. The method makes it possible to preserve the dynamics of the coupling constraints when necessary as well as to avoid breaking C1 smoothness at communication times, and also to adapt the co-simulation step size in a way that is robust both to zero-crossing variables (contrary to classical relative error-based criteria) and to jumps. Two test cases are presented to illustrate the robustness of the F3ORNITS method as well as its higher accuracy than the non-iterative Jacobi coupling algorithm (the most commonly used method in industry) for a smaller number of co-simulation steps.