Continuous approximation techniques for co‐simulation methods: Analysis of numerical stability and local error. Issue 9 (21st January 2016) - Busch, Martin
Abstract : Classical approximation techniques based on extrapolation entail a discontinuity in the equations in each macro time step which can slow down the numerical time integration. In the paper at hand a C 0 ‐continuous technique for approximating the coupling variables is reconsidered and the numerical stability and the local error of the method are compared to the classical Lagrange approximation approach. Further, the method is enhanced to a C 1 ‐continuous (continuous and differentiable) approximation technique. Both methods are investigated in combination with different numerical coupling approaches (sequential Gauss‐Seidel scheme, parallel Jacobi scheme, force/displacement coupling, displacement/displacement coupling ) which are commonly applied for co‐simulation in technical applications. Abstract : Coupling multiphysical systems by means of a co‐simulation, the data between the subsystems are interchanged at a discrete macro time grid, also denoted as communication time grid. Between the communication points the coupling variables are approximated so that the numerical solvers in the subsystems can calculate the differential equations. Classical approximation techniques based on extrapolation entail a discontinuity in the equations in each macro time step which can slow down the numerical time integration. In the paper at hand a C 0 ‐continuous technique for approximating the coupling variables is reconsidered and the numerical stability and the local error of the method are compared to the classical Lagrange approximation approach. Further, the method is enhanced to a C 1 ‐continuous (continuous and differentiable) approximation technique. Both methods are investigated in combination with different numerical coupling approaches (sequential Gauss‐Seidel scheme, parallel Jacobi scheme, force/displacement coupling, displacement/displacement coupling ) which are commonly applied for co‐simulation in technical applications. It is shown that the C 1 ‐continuous approximation technique yields a similar numerical stability and a similar local error as the Lagrange approach which results in a comparable or even better overall performance (taking into account the advantage of continuity at the numerical calculation of the subsystem differential equations). Applying the C 0 ‐continuous approach, a similar numerical stability is obtained. However, the order of the local error is significantly lower than for the C 1 ‐continuous method and the Lagrange approach.