Predictor/corrector co-simulation approaches for solver coupling with algebraic constraints

In the paper at hand, co‐simulation approaches are analyzed for coupling two solvers. The solvers are assumed to be coupled by algebraic constraint equations. We discuss 2 different coupling methods. Both methods are semi‐implicit, i.e. they are based on a predictor/corrector approach. Method 1 makes use of the well‐known Baumgarte‐stabilization technique. Method 2 is based on a weighted multiplier approach. For both methods, we investigate formulations on index‐3, index‐2 and index‐1 level and analyze the convergence, the numerical stability and the numerical error. The presented approaches require Jacobian matrices. Since only partial derivatives with respect to the coupling variables are needed, calculation of the Jacobian matrices may very easily be calculated numerically and in parallel with the predictor step. For that reason, the presented methods can in a straightforward manner be applied to couple commercial simulation tools without full solver access. The only requirement on the subsystem solvers is that the macro‐time step can be repeated once in order to accomplish the corrector step. Within the paper, we introduce methods for coupling mechanical systems. The presented approaches can, however, also be applied to couple arbitrary non‐mechanical dynamical systems. In the paper at hand, co‐simulation approaches are analyzed for coupling two solvers. The solvers are assumed to be coupled by algebraic constraint equations. The authors discuss 2 different coupling methods. Both methods are semi‐implicit, i.e. they are based on a predictor/corrector approach. Method 1 makes use of the well‐known Baumgarte‐stabilization technique. Method 2 is based on a weighted multiplier approach. For both methods, they investigate formulations on index‐3, index‐2 and index‐1 level and analyze the convergence, the numerical stability and the numerical error.