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

Abstract

This paper introduces the F $$_3$$ ORNITS non-iterative co-simulation algorithm in which F $$_3$$ 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 require it. The motivation of the F $$_3$$ ORNITS method is to accept any kind of co-simulation model as far as they represent circuits (0D models, such as ODE or DAE), including any kind of subsystem (open circuits), regardless on their available capabilities. Indeed, one of 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 $$C^1$$ 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. Five test cases are presented to illustrate the robustness of the F $$_3$$ ORNITS 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.