Summary Simulation approaches for fluid‐structure‐contact interaction, especially if requested to be consistent even down to the real contact scenarios, belong to the most challenging and still unsolved problems in computational mechanics. The main challenges are 2‐fold—one is to have a correct physical model for this scenario, and the other is to have a numerical method that is capable of working and being consistent down to a zero gap. Moreover, when analyzing such challenging setups of fluid‐structure interaction, which include contact of submersed solid components, it gets obvious that the influence of surface roughness effects is essential for a physical consistent modeling of such configurations. To capture this system behavior, we present a continuum mechanical model that is able to include the effects of the surface microstructure in a fluid‐structure‐contact interaction framework. An averaged representation for the mixture of fluid and solid on the rough surfaces, which is of major interest for the macroscopic response of such a system, is introduced therein. The inherent coupling of the macroscopic fluid flow and the flow inside the rough surfaces, the stress exchange of all contacting solid bodies involved, and the interaction between fluid and solid are included in the construction of the model. Although the physical model is not restricted to finite element–based methods, a numerical approach with its core based on the cut finite element method, enabling topological changes of the fluid domain to solve the presented model numerically, is introduced. Such a cut finite element method–based approach is able to deal with the numerical challenges mentioned above. Different test cases give a perspective toward the potential capabilities of the presented physical model and numerical approach.

Summary Cut finite element method–based approaches toward challenging fluid‐structure interaction (FSI) are proposed. The different considered methods combine the advantages of competing novel Eulerian (fixed grid) and established arbitrary Lagrangian‐Eulerian (moving mesh) finite element formulations for the fluid. The objective is to highlight the benefit of using cut finite element techniques for moving‐domain problems and to demonstrate their high potential with regard to simplified mesh generation, treatment of large structural motions in surrounding flows, capturing boundary layers, their ability to deal with topological changes in the fluid phase, and their general straightforward extensibility to other coupled multiphysics problems. In addition to a pure fixed‐grid FSI method, advanced fluid‐domain decomposition techniques are also considered, leading to highly flexible discretization methods for the FSI problem. All stabilized formulations include Nitsche‐based weak coupling of the phases supported by the ghost penalty technique for the flow field. For the resulting systems, monolithic solution strategies are presented. Various two‐ and three‐dimensional FSI cases of different complexity levels validate the methods and demonstrate their capabilities and limitations in different situations.

We present a consistent approach that allows to solve challenging general nonlinear fluid-structure-contact interaction (FSCI) problems. The underlying formulation includes both "no-slip" fluid-structure interaction as well as frictionless contact between multiple elastic bodies. The respective interface conditions in normal and tangential orientation and especially the role of the fluid stress within the region of closed contact are discussed for the general problem of FSCI. A continuous transition of tangential constraints from no-slip to frictionless contact is enabled by using the general Navier condition with varying slip length. Moreover, the fluid stress in the contact zone is obtained by an extension approach as it plays a crucial role for the lift-off behavior of contacting bodies. With the given continuity of the formulation, continuity of the discrete system of equations for any variation of the coupled system state (which is essential for the convergence of Newton's method) is reached naturally. As topological changes of the fluid domain are an inherent challenge in FSCI configurations, a noninterface fitted cut finite element method (CutFEM) is applied to discretize the fluid domain. All interface conditions, that is the "no-slip" FSI, the general Navier condition, and frictionless contact are incorporated using Nitsche based methods, thus retaining the consistency of the model. To account for the strong interaction between the fluid and solid discretization, the overall coupled discrete system is solved monolithically. Numerical examples of varying complexity are presented to corroborate the developments. In a first example, the fundamental properties of the presented formulation such as the contacting and lift-off behavior, the mass conservation, and the influence of the slip length for the general Navier interface condition are analyzed. Beyond that, two more general examples demonstrate challenging aspects such as topological changes of the fluid domain, large contacting areas, and underline the general applicability of the presented method.

The focus of this contribution is the numerical treatment of interface coupled problems concerning the interaction of incompressible fluid flow and permeable, elastic structures. The main emphasis is on extending the range of applicability of available formulations on especially three aspects. These aspects are the incorporation of a more general poroelasticity formulation, the use of the cut finite element method (CutFEM) to allow for large interface motion and topological changes of the fluid domain, and the application of a novel Nitsche-based approach to incorporate the Beavers-Joseph (-Saffmann) tangential interface condition. This last aspect allows one to extend the practicable range of applicability of the proposed formulation down to very low porosities and permeabilities which is important in several examples in application. Different aspects of the presented formulation are analyzed in a numerical example including spatial convergence, the sensitivity of the solution to the Nitsche penalty parameters, varying porosities and permeabilities, and a varying Beavers-Joseph interface model constant. Finally, a numerical example analyzing the fluid induced bending of a poroelastic beam provides evidence of the general applicability of the presented approach.C. Ager et al. / 1-25 2 mechanics model valid for "small" deformation. In the fluid domain, the Stokes equations [3,5,7,8] or, including the effect of convection, the Navier-Stokes equations [4,6] are applied. On the fluid-poroelastic interface, either the Beavers-Joseph-Saffmann [3][4][5]7] or a "no-slip" condition [5,6,8] in tangential interface direction are consulted. Details on these interface conditions for the coupling of fluid and (rigid-)porous flow can be found in [10][11][12][13][14] and the references therein.Motivated by the specific requirements of a fluid-poroelastic interaction (FPI) formulation to model rough surface contact in fluid-structure interaction (as in [2]), we extend the range of applicability of these formulations by several aspects. First, a more general formulation for the poroelastic domain, which is based on the same fundamental physical equations as the classical Biot-system, is applied. This formulation allows one to take into account large deformation and the motion of the poroelastic domain, a wide variety of material models by arbitrary strain energy density functions, and varying deformation dependent porosity (see [15][16][17] for details on this formulation and [18] for fundamentals). Second, in order to allow for large deformation and motion or even topological changes of the fluid domain, a cut finite element method (CutFEM) is applied. Herein, a non-interface-fitted, fixed-grid Eulerian computational mesh for the fluid domain is combined with an interface fitted computational mesh of the poroelastic domain in Lagrangian description w.r.t. the displacements of the poroelastic solid phase. Development of the CutFEM, as it will be applied to fluid equations, started by analyses on the Poisson equation [19], the Stok...

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Summary A novel method for complex fluid‐structure interaction (FSI) involving large structural deformation and motion is proposed. The new approach is based on a hybrid fluid formulation that combines the advantages of purely Eulerian (fixed‐grid) and arbitrary Lagrangian‐Eulerian (ALE) moving mesh formulations in the context of FSI. The structure, as commonly given in Lagrangian description, is surrounded by a fine resolved layer of fluid elements based on an ALE‐framework. This ALE‐fluid patch, which is embedded in a Eulerian background fluid domain, follows the deformation and motion of the structural interface. This approximation technique is not limited to finite element methods but can also be realized within other frameworks like finite volume or discontinuous Galerkin methods. In this work, the surface coupling between the two disjoint fluid subdomains is imposed weakly using a stabilized Nitsche's technique in a cut finite element method (CutFEM) framework. At the fluid‐solid interface, standard weak coupling of node‐matching or nonmatching finite element approximations can be utilized. As the fluid subdomains can be meshed independently, a sufficient mesh quality in the vicinity of the common fluid‐structure interface can be assured. To our knowledge, the proposed method is the only method (despite some overlapping domain decomposition approaches that suffer from other issues) that allows for capturing boundary layers and flow detachment via appropriate grids around largely moving and deforming bodies. In contrast to other methods, it is possible to do this, eg, without the necessity of costly remeshing procedures. A clear advantage over existing overlapping domain decomposition methods consists in the sharp splitting of the fluid domain, which comes along with improved convergence behavior of the resulting monolithic FSI system. In addition, it might also help to save computational costs as now background grids can be much coarser. Various FSI‐cases of rising complexity conclude the work. For validation purpose, results have been compared to simulations using a classical ALE‐fluid description or purely fixed‐grid CutFEM‐based schemes.

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