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Stabilized implicit co-simulation methods: solver coupling based on constitutive laws

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Abstract

The numerical stability of implicit (semi-implicit) predictor/corrector co-simulation methods, where the subsystem solvers are coupled by applied forces/torques (i.e., by constitutive equations), has recently been examined by Schweizer and Lu (Arch Appl Mech, 2014. doi:10.1007/s00419-014-0883-5) and Schweizer et al. (J Comput Nonlinear Dyn, 2014. doi:10.1115/1.4028503). Here, we present implicit (semi-implicit) co-simulation methods with improved stability properties. Enhanced stability behavior can be achieved by extending the coupling conditions, i.e., by taking into account derivatives and integrals of the constitutive equations. The stability of the presented co-simulation methods is analyzed by means of a co-simulation test model, which represents two coupled Dahlquist equations. By discretizing the test model with a co-simulation approach, a linear recurrence equation system is obtained, the stability of which defines the numerical stability of the underlying co-simulation method. Results are presented for the three possible decomposition approaches, namely for force/force, force/displacement and displacement/displacement decomposition. Here, co-simulation methods are derived for coupling two mechanical systems. The presented methods may, however, also be applied to couple arbitrary non-mechanical systems.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Institute of Applied Dynamics, Technical University Darmstadt, Otto-Berndt-Strasse 2, 64287, Darmstadt, Germany

    Bernhard Schweizer, Pu Li, Daixing Lu & Tobias Meyer

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  1. Bernhard Schweizer
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  2. Pu Li
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  3. Daixing Lu
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  4. Tobias Meyer
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Correspondence to Bernhard Schweizer.

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Schweizer, B., Li, P., Lu, D. et al. Stabilized implicit co-simulation methods: solver coupling based on constitutive laws. Arch Appl Mech 85, 1559–1594 (2015). https://doi.org/10.1007/s00419-015-0999-2

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