Goal-oriented error estimation and adaptivity for fluid–structure interaction using exact linearized adjoints

van der Zee, K.G., van Brummelen, E.H., Akkerman, I. and De Borst, R. (2011) Goal-oriented error estimation and adaptivity for fluid–structure interaction using exact linearized adjoints. Computer Methods in Applied Mechanics and Engineering, 200(37-40), pp. 2738-2757. (doi: 10.1016/j.cma.2010.12.010)

Abstract

We develop duality-based a posteriori error estimates for functional outputs of solutions of steady fluid–structure-interaction problems. The crucial complication in obtaining these estimates pertains to the derivation of the coupled dual (exact linearized adjoint) problem owing to the free-boundary character of fluid–structure interaction. We present two approaches to derive the dual problem. In the domain-map linearization approach, the fluid subproblem is first transformed to a fixed reference domain, after which one essentially linearizes with respect to the domain transformation map. In the shape-linearization approach, fluid unknowns are fixed in the current configuration and a very weak formulation of the fluid subproblem is then linearized using shape-derivative techniques. We show that the dual problems correspond to coupled fluid–structure problems with nonstandard coupling conditions. Furthermore, we present numerical experiments that demonstrate the consistency of the dual-based error estimates and their usefulness in goal-oriented adaptive mesh-refinement.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: De Borst, Professor Rene
• Authors: van der Zee, K.G., van Brummelen, E.H., Akkerman, I., and De Borst, R.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Computer Methods in Applied Mechanics and Engineering
• ISSN: 0045-7825
• ISSN (Online): 1879-2138
• Published Online: 23 December 2010