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

机译:使用精确线性化的伴随物进行面向目标的误差估计和流固耦合的适应性

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摘要

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.
机译:我们为稳定的流固耦合问题的解决方案的功能输出开发基于对偶的后验误差估计。由于流体-结构相互作用的自由边界特性,获得这些估计值的关键复杂之处在于耦合对偶(精确线性化伴随)问题的推导。我们提出两种方法来导出对偶问题。在域图线性化方法中,首先将流体子问题转换为固定的参考域,然后再相对于域转换图进行线性化。在形状线性化方法中,将流体未知数固定在当前配置中,然后使用形状导数技术将非常弱的流体子问题公式线性化。我们表明,双重问题对应于非标准耦合条件下的耦合流体结构问题。此外,我们目前的数值实验证明了对偶误差估计的一致性及其在面向目标的自适应网格细化中的有用性。

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