Abstract
Co-simulation methods are used to couple two or more subsystem solvers in time domain. Considering mechanical systems, the subsystems can be coupled in two different ways, namely either by applied forces/torques (i.e., by physical force/torque laws) or by constraint forces/torques (i.e., by algebraic constraint equations). Here, we present and analyze a semi-implicit co-simulation method for the case that the subsystems are coupled by applied forces/torques. The semi-implicit approach (predictor/corrector approach) analyzed here is more stable than explicit coupling methods and numerically more efficient than full-implicit coupling schemes. Furthermore, the approach takes only into account partial derivatives of the state variables with respect to the coupling variables so that the Jacobian matrix, which is required for the corrector step, has very small dimensions. For that reason, this semi-implicit approach can be implemented very easily and very time-efficiently, especially for the case that commercial codes without full solver access have to be coupled. Within this paper, we focus on mechanical systems. However, the presented method may also be applied to couple arbitrary non-mechanical systems and arbitrary solvers.
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Schweizer, B., Lu, D. Semi-implicit co-simulation approach for solver coupling. Arch Appl Mech 84, 1739–1769 (2014). https://doi.org/10.1007/s00419-014-0883-5
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DOI: https://doi.org/10.1007/s00419-014-0883-5