基于$H(\text{div})$协调有限元的流固耦合分析
Fluid-structure interaction with $H(\text{div})$-conforming finite elements
摘要：
本文提出了一种新的应用（高阶）$H(\text{div})$协调的杂交间断伽辽金有限元方法的整体流固耦合（FSI）。任意拉格朗日欧拉（ALE）描述推导出$H(\text{div})$协调有限元包括Piola变换，产生精确的发散自由流体速度的解决方案。通过Turek和Hron [50]提出的基准问题证明了所产生的方法。通过hp-细化策略，克服了奇异性和边界层，从而获得最佳空间收敛速率。
英文摘要：
In this paper a novel application of the (high-order) $H(\text{div})$-conforming Hybrid Discontinuous Galerkin finite element method for monolithic fluid-structure interaction (FSI) is presented. The Arbitrary Lagrangian Eulerian (ALE) description is derived for $H(\text{div})$-conforming finite elements including the Piola transformation, yielding exact divergence free fluid velocity solutions. The arising method is demonstrated by means of the benchmark problems proposed by Turek and Hron [50]. With hp-refinement strategies singularities and boundary layers are overcome leading to optimal spatial convergence rates.
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