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Non‐intrusive model reduction is a promising solution to system dynamics prediction, especially in cases where data are collected from experimental campaigns or proprietary software simulations. In this work, we present a method for non‐intrusive model reduction applied to Fluid‐Structure Interaction (FSI) problems. The approach is based on the a priori known sparsity of the full‐order system operators, which is dictated by grid adjacency information. In order to enforce this type of sparsity, we solve a "local", regularized least‐squares problem for each degree of freedom on a grid, considering only the training data from adjacent degrees of freedom (DoFs), thus making computation and storage of the inferred full‐order operators feasible. After constructing the non‐intrusive, sparse full‐order model (FOM), Proper Orthogonal Decomposition (POD) is used for its projection to a reduced dimension subspace and thus the construction of a reduced‐order model (ROM). The methodology is applied to the challenging Hron‐Turek benchmark FSI3, for Re = 200. A physics‐informed, non‐intrusive ROM is constructed to predict the two‐way coupled dynamics of a solid with a deformable, slender tail, subject to an incompressible, laminar flow. Results considering the accuracy and predictive capabilities of the inferred reduced models are discussed. [ABSTRACT FROM AUTHOR]

We consider nonspherical rigid body particles in an incompressible fluid in the regime where the particles are too large to assume that they are simply transported with the fluid without back‐coupling and where the particles are also too small to make fully resolved direct numerical simulations feasible. Unfitted finite element methods with ghost‐penalty stabilization are well suited to fluid‐structure‐interaction problems as posed by this setting, due to the flexible and accurate geometry handling and for allowing topology changes in the geometry. In the computationally underresolved setting posed here, accurate computations of the forces by their boundary integral formulation are not viable. Furthermore, analytical laws are not available due to the shape of the particles. However, accurate values of the forces are essential for realistic motion of the particles. To obtain these forces accurately, we train an artificial deep neural network using data from prototypical resolved simulations. This network is then able to predict the force values based on information which can be obtained accurately in an underresolved setting. As a result, we obtain forces on very coarse and underresolved meshes which are on average an order of magnitude more accurate compared with the direct boundary‐integral computation from the Navier–Stokes solution, leading to solid motion comparable to that obtained on highly resolved meshes that would substantially increase the simulation costs. [ABSTRACT FROM AUTHOR]

A temporal homogenization approach for the numerical simulation of atherosclerotic plaque growth is extended to fully coupled fluid‐structure interaction (FSI) simulations. The numerical results indicate that the two‐scale approach yields significantly different results compared to a simple heuristic averaging, where only stationary long‐scale FSI problems are solved, confirming the importance of incorporating stress variations on small time‐scales. In the homogenization approach, a periodic fine‐scale problem, which is periodic with respect to the heart beat, has to be solved for each long‐scale time step. Even if no exact initial conditions are available, periodicity can be achieved within only 2–3 heart beats by simple time‐stepping. [ABSTRACT FROM AUTHOR]

We evaluate a number of different finite-element approaches for fluid–structure (contact) interaction problems against data from physical experiments. This consists of trajectories of single particles falling through a highly viscous fluid and rebounding off the bottom fluid tank wall. The resulting flow is in the transitional regime between creeping and turbulent flows. This type of configuration is particularly challenging for numerical methods due to the large change in the fluid domain and the contact between the wall and the particle. In the finite-element simulations, we consider both rigid body and linear elasticity models for the falling particles. In the first case, we compare the results obtained with the well-established Arbitrary Lagrangian–Eulerian (ALE) approach and an unfitted moving domain method together with a simple and common approach for contact avoidance. For the full fluid–structure interaction (FSI) problem with contact, we use a fully Eulerian approach in combination with a unified FSI-contact treatment using Nitsche's method. For higher computational efficiency, we use the geometrical symmetry of the experimental setup to reformulate the FSI system into two spatial dimensions. Finally, we show full three-dimensional ALE computations to study the effects of small perturbations in the initial state of the particle to investigate deviations from a perfectly vertical fall observed in the experiment. The methods are implemented in open-source finite element libraries, and the results are made freely available to aid reproducibility. [ABSTRACT FROM AUTHOR]

Fluid‐structure interaction models involve parameters that describe the solid and the fluid behavior. In simulations, there often is a need to vary these parameters to examine the behavior of a fluid‐structure interaction model for different solids and different fluids. For instance, a shipping company wants to know how the material, a ship's hull is made of, interacts with fluids at different Reynolds and Strouhal numbers before the building process takes place. Also, the behavior of such models for solids with different properties is considered before the prototype phase. A parameter‐dependent linear fluid‐structure interaction discretization provides approximations for a bundle of different parameters at one step. Such a discretization with respect to different material parameters leads to a big block‐diagonal system matrix that is equivalent to a matrix equation as discussed in [1]. The unknown is then a matrix which can be approximated using a low‐rank approach that represents the iterate by a tensor. This paper discusses a low‐rank GMRES variant and a truncated variant of the Chebyshev iteration. Bounds for the error resulting from the truncation operations are derived. Numerical experiments show that such truncated methods applied to parameter‐dependent discretizations provide approximations with relative residual norms smaller than 10−8 within a twentieth of the time used by individual standard approaches. [ABSTRACT FROM AUTHOR]

Mathematical modeling and simulation of fluid-structure interaction problems are in the focus of research already for a longer period. However, taking into account also chemical reactions, leading to structural changes, including changes of mechanical properties of the solid phase, is rather new but for many applications is highly important area. This paper formulates a model system for reactive flow and transport in a vessel system, the penetration of chemical substances into the solid wall. Inside the wall, reactions take place that lead to changes of volume and of the mechanical properties of the wall. Numerical algorithms are developed and used to simulate the dynamics of such a mechano-chemical fluid-structure interaction problem. As a proof of concept scenario, plaque formation in blood vessels is chosen. The arbitrary Lagrangian Eulerian approach (ALE) is chosen to solve the systems numerically. Temporal discretization of the fully coupled monolithic model is accomplished by backward Euler scheme and spatial discretization by stabilized finite elements. The numerical approach is verified by numerical tests, and effective methods to maintain mesh qualities under large deformations are described. For realistic system parameters, the simulations show that the plaque formation in blood vessel is a long-time effect. The time scale of the formation is in the simulation of comparable order as in reality. [ABSTRACT FROM AUTHOR]

We present a monolithic geometric multigrid solver for fluid-structure interaction problems in Arbitrary Lagrangian Eulerian coordinates. The coupled dynamics of an incompressible fluid with nonlinear hyperelastic solids gives rise to very large and ill-conditioned systems of algebraic equations. Direct solvers usually are out of question because of memory limitations, and standard coupled iterative solvers are seriously affected by the bad condition number of the system matrices. The use of partitioned preconditioners in Krylov subspace iterations is an option, but the convergence will be limited by the outer partitioning. Our proposed solver is based on a Newton linearization of the fully monolithic system of equations, discretized by a Galerkin finite element method. Approximation of the linearized systems is based on a monolithic generalized minimal residual method iteration, preconditioned by a geometric multigrid solver. The special character of fluid-structure interactions is accounted for by a partitioned scheme within the multigrid smoother only. Here, fluid and solid field are segregated as Dirichlet-Neumann coupling. We demonstrate the efficiency of the multigrid iteration by analyzing 2d and 3d benchmark problems. While 2d problems are well manageable with available direct solvers, challenging 3d problems highly benefit from the resulting multigrid solver. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we present a Fully Eulerian framework for fluid–structure interaction (fsi) problems coupling the incompressible Navier–Stokes equations with a hyperelastic solid. The Fully Eulerian framework is a monolithic implicit variational formulation for the coupled problem. In contrast to the well-established Arbitrary Lagrangian Eulerian (ALE) coordinates, the Fully Eulerian framework formulates both subproblems, fluid and solid, in Eulerian coordinates. This concept circumvents various difficulties connected to ALE coordinates since no artificial domain mapping is used. The formulation is an interface-capturing method and uses an extension of the solid’s deformation, the Initial Point Set, to detect the interface location. By construction, very large deformation as well as topology changes like contact of the solid to the domain boundary or other solid parts are possible. [Copyright &y& Elsevier]