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Goal-oriented error estimation and adaptivity for fluid-structure interaction using exact linearized adjoints
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DOI：10.1016/j.cma.2010.12.010.png)
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Abstract
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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 ad joint) 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. (C) 2010 Elsevier B.V. All rights reserved.
Keywords:
Fluid-structure interaction
A posteriori error estimation
Duality
Exact linearized adjoint
Shape derivative
Adaptive mesh-refinement
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