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Fluid-structure interactions (FSI), i.e., the interplay of some moveable or deformable structure with an internal or surrounding fluid, are among the most widespread and most challenging coupled or multi-physics problems. Although much has been accomplished in developing good computational FSI methods and despite convincing solutions to a number of classes of problems including those presented in this book, there is a need for more comprehensive studies showing that the computational methods proposed are reliable, robust, and efficient beyond the classes of problems they have successfully been applied to.This volume of LNCSE, a sequel to vol. 53, which contained, among others, the first numerical benchmark for FSI problems and has received considerable attention since then, presents a collection of papers from the "First International Workshop on Computational Engineering - special focus FSI," held in Herrsching in October 2009 and organized by three DFG-funded consortia. The papers address all relevant aspects of FSI simulation and discuss FSI from the mathematical, informatical, and engineering perspective.

Inhaltsverzeichnis

Frontmatter

Multi-Level Accelerated Sub-Iterations for Fluid-Structure Interaction

Computational fluid-structure interaction is most commonly performed using a partitioned approach. For strongly coupled problems sub-iterations are required, increasing computational time as flow and structure have to be resolved multiple times every time step. Many sub-iteration techniques exist that improve robustness and convergence, although still flow and structure problems have to be solved a number of times every time step. In this paper we apply a multilevel acceleration technique, which is based on the presumed existing multigrid solver for the flow domain, to a two-dimensional strongly coupled laminar and turbulent problem and investigate the combination of multilevel acceleration with the Aitken underrelaxtion technique. It is found that the value for the under-relaxation parameter is not significantly different when performing sub-iterations purely on the coarse level or purely on the fine level. Therefore coarse and fine level sub-iterations are used alternately, where it is found that performing 3 or 4 coarse level sub-iterations followed by 1 fine level sub-iteration resulted in the highest gain in efficiency. Although the total number of sub-iterations increases slightly by 30%, the number of fine grid iterations can be decreased by as much as 65–70%.
A. H. van Zuijlen, H. Bijl

A Classification of Interface Treatments for FSI

This paper proposes a taxonomy of methods for the treatment of the fluid-structure interface in FSI coupled problems. The top-level classification is based on the presence or absence of Additional Interface Variables (AIV) as well as their type. Associated prototype methods: Direct Force Motion Transfer (DFMT), Mortar and Localized Lagrange Multipliers (LLM) are defined. These are later studied in more detail using a specific FSI benchmark problem used in Ross’ 2006 thesis. Desirable attributes of the interfacing methods are stated and commented upon.
C. A. Felippa, K. C. Park, M. R. Ross

Computer Modeling and Analysis of the Orion Spacecraft Parachutes

We focus on fluid-structure interaction (FSI) modeling of the ringsail parachutes to be used with the Orion spacecraft. The geometric porosity of the ringsail parachutes with ring gaps and sail slits is one of the major computational challenges involved in FSI modeling. We address the computational challenges with the latest techniques developed by the Team for Advanced Flow Simulation and Modeling (T ⋆ AFSM) in conjunction with the Stabilized Space–Time Fluid–Structure Interaction (SSTFSI) technique. We investigate the performance of the three possible design configurations of the parachute canopy, carry out parametric studies on using an over-inflation control line (OICL) intended for enhancing the parachute performance, discuss rotational periodicity techniques for improving the geometric-porosity modeling and for computing good starting conditions for parachute clusters, and report results from preliminary FSI computations for parachute clusters. We also present a stability and accuracy analysis for the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) formulation, which is the core numerical technology of the SSTFSI technique.
K. Takizawa, C. Moorman, S. Wright, T. E. Tezduyar

Stability Issues in Partitioned FSI Calculations

In this chapter a short review will be given on stability issues for fluid-structure interaction (FSI) problems we encountered and studied in the last decade. Based on this, the ideas behind two implicit coupling algorithms, developed in the department, will be explained. The first algorithm is the Interface Quasi-Newton coupling method and the second is the Interface Artificial Compressibility coupling method. Most of the applications that are shown are in the biomechanical field. These are representative for more general strongly coupled problems with incompressible fluids and flexible structures.
J. Vierendeels, J. Degroote, S. Annerel, R. Haelterman

Hydroelastic Analysis and Response of Pontoon-Type Very Large Floating Structures

Pontoon-type very large floating structures (VLFS) are giant plates resting on the sea surface. As these structures have a large surface area and a relatively small depth, they behave elastically under wave action. This type of fluid-structure interaction has being termed hydroelasticity. Hydroelastic analysis is thus necessary to be carried out for VLFS designs in order to assess the dynamic motion and stresses due to wave action. This paper presents the mathematical formulation for the hydroelastic analysis of VLFS. Hydroelastic responses and mitigation methods in reducing the structural response are discussed using some example problems.
C. M. Wang, Z. Y. Tay

Efficient Numerical Simulation and Optimization of Fluid-Structure Interaction

The paper concerns the efficient numerical simulation and optimization of fluid-structure interaction (FSI) problems. The basis is an implicit partitioned solution approach involving the finite-volume flow solver FASTEST, the finite-element structural solver FEAP, and the coupling interface MpCCI. Special emphasis is given to the grid moving techniques for which algebraic and elliptic approaches are considered. The possibilities for accelerating the computations by the usage of multigrid methods, adaptive underrelaxation, and displacement prediction are discussed. A concept for integrating the FSI solver into an optimization procedure for FSI problems is presented. Numerical results are given to illustrate the capabilities of the approaches considered.
M. Schäfer, D. C. Sternel, G. Becker, P. Pironkov

An Adaptive Finite Element Method for Fluid-Structure Interaction Problems Based on a Fully Eulerian Formulation

In this article, we continue the investigation of the general variational framework for the adaptive finite element approximation of fluid-structure interaction problems proposed in Dunne [12] and Dunne & Rannacher [13]. The modeling is based on an Eulerian description of the (incompressible) fluid as well as the (elastic) structure dynamics. This approach uses a technique which is similar to the Level Set method in the simulation of two-phase flows in so far that it also tracks initial data and from this determines to which “phase” a point belongs. The advantage is that, in contrast to the common ALE approach, the computation takes place on fixed, though dynamically adapted, reference meshes what avoids the critical degeneration in case of large deformation or boundary contact of the structure. Based on this monolithic model of the fluid-structure interaction, we apply the Dual Weighted Residual (DWR) Method for goal-oriented a posteriori error estimation and mesh adaptation to fluid-structure interaction problems. Several test examples are presented in order to illustrate the potential of this approach.
R. Rannacher, T. Richter

Numerical Simulation and Benchmarking of a Monolithic Multigrid Solver for Fluid-Structure Interaction Problems with Application to Hemodynamics

An Arbitrary Lagrangian-Eulerian (ALE) formulation is applied in a fully coupled monolithic way, considering the fluid-structure interaction (FSI) problem as one continuum. The mathematical description and the numerical schemes are designed in such a way that general constitutive relations (which are realistic for biomechanics applications) for the fluid as well as for the structural part can be easily incorporated. We utilize the LBB-stable finite element pairs Q 2 P 1 and P 2 + P 1 for discretization in space to gain high accuracy and perform as time-stepping the 2nd order Crank-Nicholson, respectively, a new modified Fractional-Step-θ-scheme for both solid and fluid parts. The resulting discretized nonlinear algebraic system is solved by a Newton method which approximates the Jacobian matrices by a divided differences approach, and the resulting linear systems are solved by direct or iterative solvers, preferably of Krylov-multigrid type.
For validation and evaluation of the accuracy and performance of the proposed methodology, we present corresponding results for a new set of FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in laminar channel flow, allowing stationary as well as periodically oscillating deformations. Then, as an example of FSI in biomedical problems, the influence of endovascular stent implantation on cerebral aneurysm hemodynamics is numerically investigated. The aim is to study the interaction of the elastic walls of the aneurysm with the geometrical shape of the implanted stent structure for prototypical 2D configurations. This study can be seen as a basic step towards the understanding of the resulting complex flow phenomena so that in future aneurysm rupture shall be suppressed by an optimal setting of the implanted stent geometry.
S. Turek, J. Hron, M. Mádlík, M. Razzaq, H. Wobker, J. F. Acker

Numerical Simulation of Fluid–Structure Interaction Using Eddy–Resolving Schemes

Eddy–resolving schemes such as large–eddy simulation (LES) or detached-eddy simulation (DES) have become popular due to their favorable capabilities of predicting complex turbulent flows. That is especially true for instantaneous flow processes involving large–scale flow structures such as separation, reattachment and vortex shedding. Flow phenomena of such kind are very often encountered when the flow around or through a device enforces the structures to be deformed or displaced, i.e. for fluid–structure interaction (FSI). The present study deals with several aspects which have to be taken into account when LES is married to FSI. That comprises the coupling scheme, the handling of moving or deformable grids and the question how their quality requirements can be achieved. A coupling scheme leading to strong coupling among flow and structure, but also maintaining the advantageous properties of explicit time–marching schemes used for LES, was set up and analyzed. Thus a new and favorable coupling procedure for FSI within the LES context was developed. This and other issues of the numerical methods applied such as the measures to maintain the grid quality are discussed in detail. Results of validation test cases of FSI in the context of rigid body motions (e.g. an elastically mounted cylinder or a swiveling flat plate) as well as benchmark results with flexible structures computed with a finite–element code are presented.
M. Münsch, M. Breuer

Partitioned Simulation of Fluid-Structure Interaction on Cartesian Grids

This contribution describes recent developments and enhancements of the coupling tool preCICE and the flow solver Peano used for our partitioned simualtions of fluid-structure interaction scenarios. Peano brings together hardware efficiency and numerical efficiency exploiting advantages of tree-structured adaptive Cartesian computational grids that, in particular, allow for a very memory-efficient implementation of parallel adaptive multilevel solvers – an efficiency which is crucial facing the large computational requirements of multi-physics applications and the recent trend in computer architectures towards multi- and many-core systems. preCICE is the successor of our coupling tool FSIsce and offers a solver-independent implementation of coupling strategies and data mapping functionalities for general multi-physics problems. The underlying client-server-like concept maintains the full flexibilty of the partitioned approach with respect to exchangeability of solvers. The data mapping relies on fast spacepartitioning tree algorithms for the detection of geometric neighbourhood relations between components of non-matching grids.
H.-J. Bungartz, J. Benk, B. Gatzhammer, M. Mehl, T. Neckel

An Explicit Model for Three-Dimensional Fluid-Structure Interaction using LBM and p-FEM

An explicit coupling model for the simulation of surface coupled fluid-structure interactions with large structural deflections is introduced. Specifically, the fluid modeled via the Lattice Boltzmann Method (LBM) is coupled to a high-order Finite Element discretization of the structure. The forces and velocities are discretely computed, exchanged and applied at the interface. The low compressibility of the Lattice Boltzmann Method allows for an explicit coupling algorithm. The proposed explicit coupling model turnes out to be accurate, very efficient and stable even for nearly incompressible flows. It was implemented in three software components: VirtualFluids (fluid), AdhoC (structure) and FSIsce (a communication library). The validity of the approach is demonstrated in two dimensions by means of comparing numerical results to measurements of an experiment. This experiment involves a flag-like structure submerged in the laminar flow field of an incompressible fluid where the structure exhibits large, geometrically non-linear, self excited, periodic motions. The methodology is then extended to three dimensions. Its performance is first demonstrated via the computation of a falling sphere in a pipe. The close correspondence of the results obtained by application of the numerical scheme compared to a semi-analytic solution is demonstrated. The proposed explicit coupling model is then extended to a plate in a cross flow. We verify the results by comparing them to results obtained by application of the commercial ALE-Finite Volume—h-FEM Fluid-Structure interaction solver Ansys Multiphysics. Additional examples demonstrate the applicability of the proposed methodology to problems of (arbitrarily) large deformations and of large scale.
S. Geller, S. Kollmannsberger, M. El Bettah, M. Krafczyk, D. Scholz, A. Düster, E. Rank

An XFEM Based Fixed-Grid Approach for 3D Fluid-Structure Interaction

This paper gives an overview on our recent research activities on a fixed grid fluid-structure interaction scheme that can be applied to the interaction of most general structures with incompressible flow. The developed approach is based on an eXtended Finite Element Method (XFEM) based strategy to allow moving interfaces on fixed Eulerian fluid grids. The enriched Eulerian fluid field and the Lagrangian structural field are partitioned and iteratively coupled using Lagrange multiplier techniques for non-matching grids. The approach allows the simulation of the interaction of thin and bulky structures exhibiting large deformations. Extensions towards automatic adaptivity and fluid boundary layer meshes are sketched and the principle applicability to contact simulations of submerged structures are presented.
W. A. Wall, A. Gerstenberger, U. Küttler, U. M. Mayer

Fluid-Structure Interaction in the Context of Shape Optimization and Computational Wind Engineering

Within this contribution, an integrated concept for the shape optimal design of light-weight and thin-walled structures like shells and membranes subject to fluid flow is presented. The Nested Analysis and Design approach is followed and a partitioned FSI simulation for the state analysis is embedded. The gained modularity allows for the adaption of the single ingredients to various technical applications by choosing appropriate coupling algorithms for the solution of the coupled problem and the sensitivity analysis as well as different strategies to describe the shapes to be optimized. A non-matching grid capability at the coupling interface supports this flexibility. The focus here is on problems of aeroelasticity in the field of Computational Wind Engineering. To ensure reliable results, investigations on the correct modeling as well as goal-oriented benchmarking are carried out. Moreover, special emphasis is given to the appropriate combination of different approaches for shape description in establishing the closed design cycle. Finally, the success of the overall solution and optimization strategy is demonstrated with an example of a hybrid, light-weight structure, subject to turbulent wind flow.
M. Hojjat, E. Stavropoulou, T. Gallinger, U. Israel, R. Wüchner, K.-U. Bletzinger

Experimental Benchmark: Self-Excited Fluid-Structure Interaction Test Cases

The swivelling motion of a flexible structure immersed in a flow can become self-excited as a result of different fluid-structure interaction mechanisms. The accurate simulation of these mechanisms still constitutes a challenge with respect to mathematical modelling, numerical discretization, solution techniques, and implementation as software tools on modern computer architectures. Thus, to support the development of numerical codes for fluid structure interaction computations, in the present work an experimental investigation on the two-dimensional self-excited periodic swivelling motion of flexible structures in both laminar and turbulent uniform flows was performed. The investigated structural model consisted of a stainless-steel flexible sheet attached to a cylindrical front body. At the trailing edge of the flexible sheet, a rectangular mass was considered. The entire structure model was free to rotate around an axle located in the central point of the front body. During the experimental investigation, the general character of the elastic-dynamic response of the structure model was studied first. The tests in laminar flows were performed in a polyglycol syrup (dynamic viscosity: 1.64 ×10−4 m{ 2}/s) for a Reynolds number smaller than 270, whereas the tests in turbulent flows were conducted in water for Reynolds numbers up to 44000. In both cases, the maximum incoming velocity tested was about 2 m/s. Subsequently, three specific test cases were selected and characterized in more detail as far as the flow velocity field and structure mechanical behavior are concerned. Thus, the present contribution presents the detailed results obtained at 1.07 m/s and at 1.45 m/s in laminar and at 0.68 m/s in turbulent flows. It also compares the experimental data with numerical results obtained for the same conditions using different simulating approaches. They revealed very good agreement in some of the fluid-structure interaction modes whereas in others deficiencies were observed that need to be analyzed in more detail.
J. Pereira Gomes, H. Lienhart

Numerical Benchmarking of Fluid-Structure Interaction: A Comparison of Different Discretization and Solution Approaches

Comparative benchmark results for different solution methods for fluid-structure interaction problems are given which have been developed as collaborative project in the DFG Research Unit 493. The configuration consists of a laminar incompressible channel flow around an elastic object. Based on this benchmark configuration the numerical behavior of different approaches is analyzed exemplarily. The methods considered range from decoupled approaches which combine Lattice Boltzmann methods with hp-FEM techniques, up to strongly coupled and even fully monolithic approaches which treat the fluid and structure simultaneously.
S. Turek, J. Hron, M. Razzaq, H. Wobker, M. Schäfer

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