Analysis of some partitioned algorithms for fluid‐structure interaction

Abstract

PurposeThe purpose of this paper is to analyse algorithms for fluid‐structure interaction (FSI) from a purely algorithmic point of view.Design/methodology/approachFirst of all a 1D model problem is selected, for which both the fluid and structural behavior are represented through a minimum number of parameters. Different coupling algorithm and time integration schemes are then applied to the simplified model problem and their properties are discussed depending on the values assumed by the parameters. Both exact and approximate time integration schemes are considered in the same framework so to allow an assessment of the different sources of error.FindingsThe properties of staggered coupling schemes are confirmed. An insight on the convergence behavior of iterative coupling schemes is provided. A technique to improve such convergence is then discussed.Research limitations/implicationsAll the results are proved for a given family of time integration schemes. The technique proposed can be applied to other families of time integration techniques, but some of the analytical results need to be reworked under this assumption.Practical implicationsThe problems that are commonly encountered in FSI can be justified by simple arguments. It can also be shown that the limit at which trivial iterative schemes experience convergence difficulties is very close to that at which staggered schemes become unstable.Originality/valueAll the results shown are based on simple mathematics. The problems are presented so to be independent of the particular choice for the solution of the fluid flow.