Fluid-structure interaction (FSI) problems are pervasive in the computational engineering community. The need to address challenging FSI problems has led to the development of a broad range of numerical methods addressing a variety of application-specific demands. While a range of numerical and experimental benchmarks are present in the literature, few solutions are available that enable both verification and spatiotemporal convergence analysis. In this paper, we introduce a class of analytic solutions to FSI problems involving shear in channels and pipes. Comprised of 16 separate analytic solutions, our approach is permuted to enable progressive verification and analysis of FSI methods and implementations, in two and three dimensions, for static and transient scenarios as well as for linear and hyperelastic solid materials. Results are shown for a range of analytic models exhibiting progressively complex behavior. The utility of these solutions for analysis of convergence behavior is further demonstrated using a previously published monolithic FSI technique. The resulting class of analytic solutions addresses a core challenge in the development of novel FSI algorithms and implementations, providing a progressive testbed for verification and detailed convergence analysis.

中文翻译：

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一类用于线性和非线性流固耦合算法验证和收敛分析的解析解

流固耦合 (FSI) 问题在计算工程界很普遍。解决具有挑战性的 FSI 问题的需要导致了广泛的数值方法的发展，以满足各种特定应用的需求。虽然文献中存在一系列数值和实验基准，但很少有解决方案能够同时进行验证和时空收敛分析。在本文中，我们介绍了一类涉及通道和管道剪切的 FSI 问题的解析解。由 16 个独立的分析解决方案组成，我们的方法经过排列，可以在二维和三个维度上对静态和瞬态场景以及线性和超弹性固体材料的 FSI 方法和实现进行渐进式验证和分析。显示了一系列表现出逐渐复杂行为的分析模型的结果。使用先前发布的单片 FSI 技术进一步证明了这些解决方案用于分析收敛行为的效用。由此产生的一类分析解决方案解决了开发新型 FSI 算法和实现的核心挑战，为验证和详细的收敛分析提供了一个渐进的测试平台。