Explicit and Implicit Solver Coupling: Stability Analysis Based on an Eight-Parameter Test Model

Coupling different solvers via co-simulation is frequently applied in the field of multi-physical simulation. The numerical stability and accuracy of the coupled problem strongly depends on the coupling technique used for the co-simulation. In the current work, different co-simulation approaches are analytically investigated based on a linear eight-parameter test model. The test model is formulated in state-space form containing input and output variables so that the results may directly be applied to practical coupling interfaces. For the test model, recurrence formulas are derived for explicit and implicit coupling techniques of Jacobian and Gauss-Seidel type. The numerical stability of the co-simulation approach is examined by an eigenvalue analysis of the corresponding recurrence equation. Three-dimensional stability plots can be analyzed for different coupling methods and for arbitrary order of the extrapolation/interpolation polynomial. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)