一类用于线性和非线性流固耦合算法验证与收敛性分析的解析解
A Class of Analytic Solutions for Verification and Convergence Analysis of Linear and Nonlinear Fluid-Structure Interaction Algorithms
AI总结：
本文提出一类含16个解析解的流固耦合测试集，支持二维/三维、静态/瞬态及线性和超弹性材料场景，用于算法验证与收敛性分析。
摘要：
流固耦合（FSI）问题在计算工程领域普遍存在。解决具有挑战性的流固耦合问题的需求促使了广泛数值方法的发展，这些方法针对各种特定应用需求。虽然文献中存在一系列数值和实验基准，但很少有解能够同时支持验证和时空收敛性分析。在本文中，我们引入了一类涉及通道和管道中剪切流的流固耦合问题的解析解。该方法由16个独立的解析解组成，通过排列组合，能够对二维和三维、静态和瞬态场景以及线性和超弹性固体材料的流固耦合方法和实现进行渐进式验证和分析。结果展示了一系列表现出逐渐复杂行为的解析模型。这些解在收敛行为分析中的实用性进一步通过先前发表的单片式流固耦合技术得到证明。所得到的解析解类别解决了新型流固耦合算法和实现开发中的核心挑战，为验证和详细收敛性分析提供了一个渐进式测试平台。
英文摘要：
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.
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