Co-simulation with variable approximation order: order control algorithm for solver coupling approaches

Abstract

Considering co-simulation and solver coupling approaches, the coupling variables have to be approximated within a macro-time step (communication-time step), e.g., by using extrapolation/interpolation polynomials. Usually, the approximation order is assumed to be fixed. The efficiency and accuracy of a co-simulation may, however, be increased by using a variable approximation order. Therefore, a technique to control the integration order is required. Here, an order control algorithm for co-simulation and solver coupling methods is presented. The order controller is incorporated into the control algorithm for the macro-step size so that co-simulations with variable integration order and variable macro-step size can be carried out. Different numerical examples are presented, which illustrate the applicability and benefit of the proposed order control strategy. This contribution mainly focuses on mechanical systems. The presented techniques may, however, also be applied to nonmechanical dynamical systems.