Algorithms for strong coupling procedures

Abstract

This paper considers algorithms for computing the response of a coupled problem with a partitioned approach. One important example treated here is fluid–structure interaction (FSI). Often procedures or even software exists to solve each sub-problem separately, and one wants to couple both. This setting seems to allow only the so-called weak coupling which is not sufficient for some problems. The so-called strong coupling is often a totally implicit formulation, where the system components are evaluated at the same time level. This usually requires an iterative procedure. The FSI problem is cast as an abstract differential algebraic equation (DAE), for which the coupling procedures are developed. With the partitioned approach, one simple and frequently used computational procedure is similar to a block-Gauss–Seidel iteration. It is shown why this approach may experience difficulties, and how they may be circumvented with Newton-like methods still staying in the partitioned framework. The functional and software engineering requirements for the simulation interface are described and analysed. Some simple coupled example problems demonstrate how the proposed procedures work.