Static correction in model order reduction techniques for multiphysical problems

Abstract

In this paper multiphysical model order reduction methods for thermomechanical problems are investigated. Different variants of modal truncation methods are outlined. A basis built of state space modes of the system represents the behavior of the system but the method requires complicated complex modes. This is why we also introduce bases built from a composition of bases of the separate uncoupled physical fields because these are simpler to build. One can improve on these bases again by inclusion of a correction for the coupling effect, for example based on a derivation from a first order perturbation analysis. These bases shows a good representation on the dynamics behavior, but generally do not give correct static results. However we want at least the static solution to be correct in order to guarantee that if the problem is quasi-static or if it converges to a steady-state static solution, one gets the exact solution. Hence one wants to add a static correction to the solution (a posteriori). That static correction can also be used to enrich the basis. In this contribution an investigation on the static residuals for different bases is performed. ©2010 Society for Experimental Mechanics Inc.