A Proposed Implementation of Tarjan's Algorithm for Scheduling the Solution Sequence of Systems of Federated Models

Tarjan's algorithm schedules the solution of systems of equations by noting the coupling and grouping between the equations. Simulating complex systems, e.g., advanced power plants, aerodynamic systems, or the multi-scale design of components, requires the linkage of large groups of coupled models. Currently, this is handled manually in systems modeling packages. That is, the analyst explicitly defines both the method and solution sequence necessary to couple the models. In small systems of models and equations this works well. However, as additional detail is needed across systems and across scales, the number of models grows rapidly. This precludes the manual assembly of large systems of federated models, particularly in systems composed of high fidelity models. This paper examines extending Tarjan's algorithm from sets of equations to sets of models. The proposed implementation of the algorithm is demonstrated using a small one-dimensional system of federated models representing the heat transfer and thermal stress in a gas turbine blade with thermal barrier coating. Enabling the rapid assembly and substitution of different models permits the rapid turnaround needed to support the “what-if” kinds of questions that arise in engineering design.