The analytical approach, which lies at the basis of the exact and natural sciences, rests on the notion that complex systems can be reduced to simple components. This divide-and-conquer approach has shaped contemporary science and technology, and has formed the foundation for virtually all scientific breakthroughs in the 19th and 20th century. It is also the origin of the separation of mechanics into fluid and solid mechanics, so much so that these branches of mechanics are commonly considered as distinct scientific disciplines. Notably, the disconnection between fluid and solid mechanics is evidenced by the tremendous advancements in computational methods and commercial simulation codes for fluid- and solid-mechanical systems separately, as compared to the relative underdevelopment of commercial codes for fluid-structure-interaction analyses.

With the advancement of analysis capabilities for fluid- and structure-mechanics systems separately, emerged the realization that many problems in science and engineering cannot be appropriately categorized as either a fluid or structure problem, but are fundamentally determined by the interaction of a fluid and a solid. Examples are flutter and buffet instabilities in aerospace and civil engineering, the functioning of heart valves in biomechanics, sloshing and vibrations in flexible fluid containers and fluid conduits, deployment of inflatable structures such as airbeams and airbags, and deformation of soft substrates due to capillary forces, for example, in microfluidic applications and biomechanics. The development of computational methods for fluid-structure-interaction problems commenced in the early 1980s and many important foundations were laid in the 1990s. Despite the significant progress that has been made since then in computational models and methods for Fluid-Structure Interaction (FSI), many open challenges still remain, and computational FSI continues to be an active area of investigation and development.

This special issue presents an overview of vanguard developments in computational methods for fluid-structure interaction. The 12 manuscripts in this special issue cover a variety of contemporary topics in computational FSI.

The development of efficient and robust partitioned solution methods continues to be an important branch of research in computational FSI. Such partitioned solution methods allow to retain the modularity of the fluid and structure subsystems, thus enabling the reuse of the complete gamut of advanced commercial and open-source simulation software for fluid-dynamics and solid-dynamics problems separately. In this special issue, Cao et al. present a spatially-varying Robin coupling condition to mitigate the added-mass effect of incompressible flows in FSI in partitioned solution procedures.¹ In a similar vein, Dettmer et al. present a new combined two-field relaxation strategy to enhance the stability of the standard Dirichlet–Neumann FSI coupling strategy in the presence of strong added-mass effects.² The work by Rüth et al. is concerned with the development of quasi-Newton waveform relaxation techniques to enable efficient and robust partitioned iterative solution strategies supporting multi-rate approximations (or subcycling), and the implementation of this multi-rate coupling strategy in the open-source coupling software preCICE.³

Another important contemporary development in computational fluid-structure interaction, pertains to FSI in conjunction with auxiliary physical subsystems. A main class of problems of this type, are fluid-structure-contact-interaction (FSCI) problems, that is, problems in which the structure subsystem exhibits (self-)contact. A fundamental challenge in FSCI problems, is that the fluid domain generally exhibits a topological change at contact. In this special issue, Hiromi-Spühler and Hoffman present a unified continuum model for fluid-structure interaction with full-friction contact with application to aortic valves.⁴ As opposed to the moving-mesh approach considered by Hiromi-Spühler and Hoffman, the manuscript by Ager et al. is concerned with an immersed (CutFEM) FSCI formulation, in which a continuous transition from the standard no-slip condition to frictionless contact is enabled by means of a generalized Navier boundary condition with variable slip coefficient.⁵ A second important class of FSI problems with auxiliary interactions, pertains to FSI of free-boundary flows, that is, FSI problems in which the fluid subsystem itself exhibits a free surface or an interface between distinct fluid components. As capillary effects on the fluid meniscus generally play a crucial role in the behavior of these problems, this class of problems is commonly referred to as elasto-capillarity or, in the case that the fluid subsystem is comprised of two distinct species separated by an interface, as binary-fluid–structure interaction (BFSI). An essential complication in elasto-capillary FSI pertains to the modeling of the contact line, that is, the triple point corresponding to the intersection of the fluid meniscus with the fluid-structure interface. Ohayon et al. present a new formulation for modeling the effects of sloshing of an acoustic fluid with a free-boundary with capillary effects in an elastic container.⁶ The manuscript by van Brummelen et al. presents an adaptive simulation framework for elasto-capillary FSI in which the fluid–fluid meniscus is modeled as a diffuse interface via the Navier–Stokes–Cahn–Hilliard equations, which intrinsically accounts for the motion of the contact line.⁷

Immersed and embedded boundary methods are taking an increasingly important position in computational FSI, by virtue of their geometric flexibility. In addition to the manuscript by Ager et al. this special issue features three manuscripts on this subject. A fundamental difficulty in immersed-FSI methods concerns the fact that the topology and geometry of the intersection of the fluid-structure interface with the background mesh evolve in an essentially arbitrary manner during the FSI dynamics, compromising stability and accuracy of the FSI formulation. Ho and Farhat present an embedded boundary method in which the fluid equations and, correspondingly, system outputs depend smoothly on the position of the interface, that is, discrete events associated with changes in the topology of the mesh-interface intersection are eliminated.⁸ Fernández and Gerosa introduce a stable coupling scheme for immersed FSI, based on a projective semi-implicit splitting paradigm in combination with a Nitsche-type formulation.⁹ Huang et al. present a special immersed-FSI approach for solid subsystems of co-dimension two, such as cables, booms and risers.¹⁰

The tremendous recent progress in computational FSI has also enabled the use of FSI simulations in multi-disciplinary control, design, optimization and inversion problems. Such control and optimization problems pose severe conditions on the stability and consistency of the FSI formulation, as well as on the efficiency of the computational procedure. In this special issue, Wick and Wollner present a monolithic formulation for gradient-based optimization for unsteady FSI problems, based on the adjoint-equation formalism.¹¹ Boncoraglio et al. consider a new model-reduction framework to enhance the efficiency of multi-parameter FSI optimization problems with linearized FSI constraints.¹²

位于精确科学和自然科学基础上的分析方法基于复杂系统可以简化为简单组件的概念。这种分而治之的方法塑造了当代科学技术，并为 19 世纪和 20 世纪几乎所有的科学突破奠定了基础。这也是将力学分为流体力学和固体力学的起源，以至于这些力学分支通常被认为是不同的科学学科。值得注意的是，与流固耦合分析商业代码的相对欠发达相比，流体力学和固体力学系统的计算方法和商业模拟代码的巨大进步证明了流体力学和固体力学之间的脱节。

随着流体力学和结构力学系统分别分析能力的提高，人们意识到科学和工程中的许多问题不能恰当地归类为流体或结构问题，而是从根本上由流体和结构的相互作用决定的。坚硬的。例如，航空航天和土木工程中的颤振和抖振不稳定性、生物力学中心脏瓣膜的功能、柔性流体容器和流体管道中的晃动和振动、气囊和气囊等充气结构的展开以及由于毛细管力引起的软基材变形例如，在微流体应用和生物力学中。流固耦合问题计算方法的发展始于 1980 年代初，许多重要的基础在 1990 年代奠定。尽管此后在流固耦合 (FSI) 的计算模型和方法方面取得了重大进展，但许多开放性挑战仍然存在，计算 FSI 仍然是一个活跃的研究和开发领域。

本期特刊概述了流固耦合计算方法的前沿发展。本期特刊中的 12 篇手稿涵盖了计算 FSI 中的各种当代主题。

开发高效且稳健的分区解法仍然是计算 FSI 研究的一个重要分支。这种分区解决方案方法允许保留流体和结构子系统的模块化，从而使先进的商业和开源模拟软件的完整色域能够分别重用于流体动力学和固体动力学问题。在这个特刊中，曹等人。提出空间变化的罗宾耦合条件，以减轻 FSI 中不可压缩流动在分区求解过程中的附加质量效应。¹同样，Dettmer 等人。提出了一种新的组合双场弛豫策略，以在存在强附加质量效应的情况下增强标准 Dirichlet-Neumann FSI 耦合策略的稳定性。² Rüth 等人的工作。关注准牛顿波形弛豫技术的开发，以实现支持多速率近似（或子循环）的高效和稳健的分区迭代解决方案策略，以及这种多速率耦合策略在开源耦合软件 preCICE 中的实现。³

计算流固耦合的另一个重要的当代发展涉及 FSI 与辅助物理子系统的结合。此类问题的主要类别是流固接触相互作用 (FSCI) 问题，即结构子系统表现出（自）接触的问题。FSCI 问题的一个基本挑战是流体域通常在接触时表现出拓扑变化。在本期特刊中，Hiromi-Spühler 和 Hoffman 提出了一个统一的连续介质模型，用于流固耦合与应用到主动脉瓣的全摩擦接触。⁴与 Hiromi-Spühler 和 Hoffman 考虑的移动网格方法相反，Ager 等人的手稿。涉及浸入式 (CutFEM) FSCI 公式，其中通过具有可变滑动系数的广义 Navier 边界条件实现从标准无滑动条件到无摩擦接触的连续过渡。⁵具有辅助相互作用的第二类重要 FSI 问题与自由边界流动的 FSI 问题有关，即流体子系统本身呈现自由表面或不同流体组分之间的界面的 FSI 问题。由于流体弯月面的毛细管效应通常在这些问题的表现中起着至关重要的作用，因此这类问题通常被称为弹性毛细管现象或者，在流体子系统由由界面分隔的两种不同物质组成的情况下，作为二元流体结构相互作用(BFSI)。弹性毛细管 FSI 中的一个基本并发症与接触线的建模有关，即对应于流体弯月面与流固界面相交的三相点。奥哈永等人。提出了一种新公式，用于模拟弹性容器中具有毛细管效应的自由边界的声学流体的晃动效应。⁶van Brummelen 等人的手稿。提出了弹性毛细管 FSI 的自适应模拟框架，其中流体 - 流体弯月面通过 Navier-Stokes-Cahn-Hilliard 方程建模为扩散界面，该方程本质上解释了接触线的运动。⁷

由于其几何灵活性，浸入式和嵌入式边界方法在计算 FSI 中占据越来越重要的地位。除了 Ager 等人的手稿。本期特刊刊登了关于这个主题的三份手稿。浸入式 FSI 方法的一个基本困难在于，在 FSI 动力学过程中，流固界面与背景网格相交的拓扑和几何形状以基本上任意的方式演变，从而影响 FSI 公式的稳定性和准确性。Ho 和 Farhat 提出了一种嵌入式边界方法，其中流体方程和相应的系统输出平滑地取决于界面的位置，即与网格界面交点拓扑变化相关的离散事件被消除。⁸ Fernández 和 Gerosa 介绍了一种用于浸入式 FSI 的稳定耦合方案，基于投影半隐式分裂范式与 Nitsche 型公式相结合。⁹黄等人。提出了一种特殊的浸入式 FSI 方法，用于双维固体子系统，例如电缆、吊杆和立管。¹⁰

最近在计算 FSI 方面取得的巨大进展也使得 FSI 模拟能够在多学科控制、设计、优化和反演问题中使用。这种控制和优化问题对 FSI 公式的稳定性和一致性以及计算过程的效率提出了严峻的条件。在本期特刊中，Wick 和 Wollner 提出了基于伴随方程形式主义的非定常 FSI 问题的基于梯度优化的整体公式。¹¹ Boncoraglio 等人。考虑一个新的模型简化框架，以提高具有线性化 FSI 约束的多参数 FSI 优化问题的效率。¹²