Abstract

Co-simulation methods are used to couple two or more solver in the time domain. Basically, two fields of application can be distinguished. Firstly, co-simulation is used in order to couple different solvers in time domain to analyze multidisciplinary systems. Secondly, co-simulation methods may be employed to parallelize a (monodisciplinary) dynamic model.

Applying a co-simulation approach, the overall system is decomposed into two (or more) subsystems. The coupling between the subsystems is defined by appropriate coupling variables, i.e. by introducing appropriate subsystem input and output variables. Furthermore, a communication-time grid has to be defined. Between the communication-time points (macro-time points T_0,T_1,…,T_N), the subsystems integrate independently. The coupling variables are only exchanged at the macro-time points between the subsystems. For the subsystem integration between the macro-time points, the coupling variables have to be approximated using appropriate extrapolation/interpolation techniques.

In this work semi-implicit co-simulation methods are presented and analyzed in terms of stability and convergence. Both procedures for coupling via constitutive equations and algebraic equations are presented. The developed methods are all based on a predictor / corrector approach, which in this work for the purpose of computation time efficiency only one corrector step is realized. Thus, the method can be regarded as semi-implicit coupling methods.

Compared to explicit methods have semi-implicit coupling method a significantly higher implementation effort. On the one hand Jacobians in each macro step must be calculated for the corrector step, on the other hand the subsystem integration has to be repeated once. The great advantage of the proposed co-simulation methods lies in the significantly improved numerical stability.