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In this contribution a powerful technique is described which allows the strong coupling of partitioned solvers in fluid-structure interaction (FSI) problems. The method allows the use of a black box fluid and structural solver because it builds up a reduced order model of the fluid and structural problem during the coupling process. Each solution of the fluid/structural solver in the coupling process can be seen as a sensitivity response of an applied displacement/pressure mode. The applied modes and their responses are used to build up the reduced order model. The method is applied on the flow in the left ventricle during the filling and emptying phase. Two to three modes are needed, depending on the moment in the heart cycle, to reduce the residual by four orders of magnitude and to achieve a fully coupled solution at each time step.

This paper discusses certain aspects of the design and implementation of , an object-oriented multi-physics finite-element library, available as open-source software at . The main aim of the library is to provide an environment that facilitates the robust, adaptive solution of multi-physics problems by monolithic discretisations, while maximising the potential for code re-use. This is achieved by the extensive use of object-oriented programming techniques, including multiple inheritance, function overloading and template (generic) programming, which allow existing objects to be (re-)used in many different ways without having to change their original implementation.

We provide an overview of the space-time finite element techniques developed by the Team for Advanced Flow Simulation and Modeling (T★AFSM) for modeling of fluid–structure interaction problems. The core method is the Deforming- Spatial-Domain/Stabilized Space-Time formulation, complemented with the mesh update methods, including the Solid-Extension Mesh Moving Technique and Move- Reconnect-Renode Mesh Update Method. Also complementing the core method are the block-iterative, quasi-direct and direct coupling methods for the solution of the fully-discretized, coupled fluid and structural mechanics equations. Additionally, the Surface-Edge-Node Contact Tracking technique is introduced as a contact algorithm for the purpose of protecting the quality of the fluid mechanics mesh between the structural surfaces coming into contact. We present mesh-moving tests and numerical examples with incompressible flows and membrane and cable structures.

Several algorithms for fluid-structure interaction are described. All of them are useful for the loose coupling of fluid and structural dynamics codes. The first class of algorithms considers the loose coupling of implicit time-marching codes. Of these, a predictor-corrector algorithm that may be interpreted as a Jacobi iteration with block-diagonal terms was found to be a good compromise of simplicity, generality and speed. The second class of algorithms treats the displacement of the surface of the structure that is in contact with the fluid. It is shown that a straightforward treatment of the displacements for arbitrary choice of timesteps can lead to instabilities. For optimal stability, at each timestep the ending time of the fluid should be just beyond the ending time of the structure. The third class of algorithms treats the movement of the flow mesh in an ALE setting. The use of a projective prediction of mesh velocities, as well as linelet preconditioning for the resulting PCG system can reduce significantly the effort required. Examples are included that show the effectiveness of the proposed procedures.

The deployment of an airbag is most fatal and dangerous to a passenger when they are in an out of position (OOP) situation, with the airbag making contact before it is fully inflated. This can lead to severe, if not life threatening, injuries to the passenger. This situation is more commonly associated with small females and children who are positioned near to the airbag module, i.e. in an OOP load cases. The aim of this research is to assess the response of a Hybrid III 5 Percentile female anthropomorphic dummy positioned in a FMVSS 208 low risk static airbag deployment OOP load cases using a transient dynamic finite element program called LS-DYNA. The simulation considers the standard procedures utilised in the LSDYNA, where assumptions such as uniform airbag pressure and temperature are made, along with a more recently developed procedure that takes into account the fluid-structure interaction between the inflating gas source and the airbag fabric, referred to as Arbitrary Lagrangain Eulerian (ALE) theory. Both simulations were compared to test data received by Jaguar, indicating satisfactory results in terms of correlation, with the more recently developed procedure, ALE theory, showing the greatest accuracy, both in terms of graphical and schematic comparison, especially in the very early stages of the inflation process. As a result, the new simulation procedure model was utilised to research into the effects of changing the designs of the airbag module.

We propose a general variational framework for the adaptive finite element approximation of fluid-structure interaction problems. The modeling is based on an Eulerian description of the (incompressible) fluid as well as the (elastic) structure dynamics. This is achieved by tracking the movement of the initial positions of all ‘material’ points. In this approach the deformation appears as a primary variable in an Eulerian framework. Our approach uses a technique which is similar to the method in so far that it also tracks initial data, in our case the set of , and from this determines to which ‘phase’ a point belongs. To avoid the need for reinitialization of the initial position set, we employ the harmonic continuation of the structure velocity field into the fluid domain. Based on this monolithic model of the fluid-structure interaction we apply the for goal-oriented a posteriori error estimation and mesh adaptation to fluid-structure interaction problems. Several stationary as well as nonstationary examples are presented.

We investigate a new method of solving the problem of fluid-structure interaction of an incompressible elastic object in laminar incompressible viscous flow. Our proposed method is based on a fully implicit, monolithic formulation of the problem in the arbitrary Lagrangian-Eulerian framework. High order FEM is used to obtain the discrete approximation of the problem. In order to solve the resulting systems a quasi-Newton method is applied with the linearized systems being approximated by the divided differences approach. The linear problems of saddle-point type are solved by a standard geometric multigrid with local multilevel pressure Schur complement smoothers.

The paper deals with an implicit partitioned solution approach for the numerical simulation of fluid-structure interaction problems. The method is realized on the basis of the finite-volume flow solver FASTEST, the finite-element structural solver FEAP, and the quasi-standard coupling interface MpCCI. Multigrid methods can be involved at different levels. The method is verified by comparisons with benchmark results. Investigations concerning the influence of the grid movement technique and an underrelaxation are presented. Results of a combined numericalexperimental study are given for validation. For the corresponding configuration also basic fluid-structure interaction mechanism are investigated.

This contribution focusses on computational approaches for fluid structure interaction problems from several perspectives. Common driving force is the desire to handle even the large deformation case in a robust, efficient and straightforward way. In order to meet these requirements main subjects are on the one hand necessary improvements on coupling issues as well as on Arbitrary Lagrangian Eulerian (ALE) approaches. On the other hand, we discuss pros and cons of avail-able fixed grid approaches and start the development of new such approaches. Some numerical examples are provided along the paper.

Despite their frequently supposed problems concerning the approximation of complicated and changing geometries, hierarchical Cartesian grids such as those defined by spacetrees have proven to be advantageous in many simulation scenarios. Probably their most important advantage is the simple, efficient, and flexible interface they offer and which allows for an elegant embedding of numerical simulations in some broader context, as it is encountered in a partitioned solution approach to coupled or multi-physics problems in general and to fluid-structure interaction in particular. For the latter, a flow solver, a structural solver, and a tool or library performing the data exchange and algorithmic interplay are required. Here, the main challenge still unsolved is to keep the balance between flexibility concerning the concrete codes used on the one hand and overall efficiency or performance on the other hand.