Influence of coupling approximation on the numerical stability of explicit co-simulation

Abstract

Co-simulation allows the parallelization of several subsystems in a distributed manner with data exchanges at discrete user-defined communication points (macro-time points). Between two macro-time points, subsystems are integrated in a local circumstance using specified solvers. By adopting the technique, the computational efficiency can be enhanced greatly without exposure of inner information. As a weak coupling, communication between subsystems is usually approximated by extrapolated or interpolated polynomials that may induce instability. Implicit or semi-implicit co-simulation with iteration of macro-time steps can improve stability behavior significantly. However, reinitialization may be unfeasible for realtime simulation or not supported by most commercial tools. Therefore, stabilized non-iterative co-simulation has been more popular that can be achieved either by appropriate communication techniques or by interface error estimations. However, the influence of the coupling approximations on numerical stability is not well understood. In this paper, the numerical stability of explicit co-simulation will be studied using different approximations of coupling techniques. The influence of communication schemes (parallel and sequential coupling scheme), least square as well as relaxation techniques using an applied force coupling approach will be investigated quantitatively with the help of a linear two-mass oscillator. A quarter car model is used to validate the stability analysis of the linear oscillator. The results indicate that by adopting appropriate coupling techniques, stability improvement can be accomplished. Higher order of extrapolation (interpolation) introduces damping to the distributed system while relaxation and least square approaches might trigger artificial oscillations.