The relevance of conservation for stability and accuracy of numerical methods for fluid?structure interaction

Numerical simulation of fluid–structure interactions has typically been done using partitioned solution methods. However, partitioned methods are inherently non-conservative and generally numerically unstable. The deficiencies of partitioned methods have motivated the investigation of monolithic solution methods. Conservation is possible for monolithic methods, the conditions have recently been presented [E.H. van Brummelen, S.J. Hulshoff, R. de Borst, Energy conservation under incompatibility for fluid–structure interaction problems, Comput. Methods Appl. Mech. Engrg. 192 (2003) 2727–2748]. In the present paper we investigate the relevance of maintaining conservation for a model fluid–structure interaction problem, viz., the piston problem. To distinguish the effect of the error induced by the interface coupling from the fluid and structure discretization errors, we use fluid subcycling and an exact time-integration method for the structure. A comparison between conservative and non-conservative monolithic methods as well as partitioned methods is made. We show that maintaining conservation has considerable impact on the stability and accuracy of the numerical method. These results also indicate that only for a conservative monolithic scheme the improvement in accuracy over partitioned methods warrants the computational cost associated with a monolithic solution. Moreover, we illustrate the implications that particular combinations of fluid and structure discretizations can have on the conservation properties of the fluid–structure interaction problem.

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